Maye worth thinking about: not every style needs to work for every battle.
For example, even if we can get a sniper strategy working - hunker down behind cover and single-shot enemies one at a time - there's no way to make it work for an escort-the-truck type mission where you're trying to guard a moving vehicle. Or an escape-from-the-horde mission. Close combat might work well in caves and urban settings but not at all in space. I'd say that's okay, though it does make planning your skills a little harder.
How can you make a sniper strategy workable? I think it needs cover (so that enemies don't even know where you are, and when they do figure it out it's still hard to hit you) plus long-range weapons. Long-range, here, means that it takes mecha with ordinary weapons a few turns to get into range to shoot back. Since a sniper mech doesn't need to move fast, these weapons can be heavy. Shots should be very accurate but maybe slow, and they should usually do enough damage to single-shot an enemy. (This is not just for thematic reasons - at high renown there will be a swarm of them who will start converging on you, and you have to be able to pick a reasonable number of them off before they catch you.) Sniper players should invest lots of skill points in accuracy and in remaining hidden.
Automatic weapons-based play kind of works now: you charge into range of your high-BV weapons, and you pour a zillion rounds into the general vicinity of your enemies. It *should* be easier to hit with high-BV weapons, although it might just be a question of rolling to-hit independently for every round (which makes it much more likely that *some* will hit). I'd say BV weapons should have a fairly short range, so that you really need to get in close (any maybe weather a few shots on the way in). Skill-wise, you don't need accuracy all that much, but you need to be able to shoot while moving, and you need to be able to dodge on the way in.
Missile/artillery: launch area-effect weapons from a distance. Area-effect weapons should be really easy to hit with (maybe even easier than they are now) but either have really heavy ammo or do not all that much damage. This should include BLAST 0 (single-square) area-effect weapons, which are now called SCATTER. I can see two ways to play this sort of game: either go in lumbering with ammo that you fire off all at once then zip around in a much lighter mech, or just plain go heavy and pummel from a moderate distance. Short-range area-effect weapons are also a way to do damage to even the most agile foes. One thing to watch out for is the combination of area effect and status: this lets even an unskilled fighter with a low-damage weapon inflict nasty status effects on an enemy.
I don't see how melee can work in space, but in caves and urban environments it could be made to work: stay under cover until you can close with an enemy, then stop and hack them to bits (ideally with a surprise attack, but possibly in a sword-to-sword duel). The trick is to keep stopped combatants from getting utterly pasted by ranged fire from enemies. I think reducing or removing the to-hit bonuses for fast mecha might help with this, or (see below) uncoupling accuracy from damage so that you get hit but not destroyed. Melee weapons should do a lot of damage, and should be light enough that mecha can also carry some ranged weapons to reduce the riffraff. In fact, a very anime mechanic would be to make melee a way to deal with very-hard-to-hit mecha: you enter a big battle and shoot down all the mooks, but you just can't hit the Big Bad, so you close with him and draw your sword. An epic duel ensues, in which he chops off the arm of your mech but you finally manage to spear him through the body...
What does this mean about skills? Well, the relative importance of accurate gunnery is different for the three roles, as is the ability to dodge. Stealth/cover is different too. I'd like to see Electronic Warfare as portable cover, maybe affecting nearby (allied) mecha as well (so that building an EW specialist mech for the team makes sense). But the exponential increase in skill costs means that if you can afford a high level of one skill, you can afford an almost-as-high level of any other skill as well. So the only real choice is that forced by the skill number limitation. Maybe instead of Fibonacci numbers, increasing you skill from level n to level n+1 could cost n*100 XP? (Or n^2*100 if that's too drastic.) This way you can afford to really specialize - you don't feel "I need 23300 XP to advance mecha piloting, why not just spend 800 on mecha fighting in the meantime?". Of course the effects of really high skill levels would have to be thought out carefully, but I'm imagining that (say) a level 16 mecha piloting would give you a +16 to hit, so that a sniper who poured all their points into gunnery would be able to reliably hit every time.
To make tanks viable, why not uncouple accuracy and damage? If I hit really accurately with a DC1x10 weapon, I should be able to do called shots, but they would still only do ~10 damage to the target. So a tank that's really easy to hit doesn't take any more damage per hit than a zippy unarmored mech. A hapless infantry mech can plink away at the tank for hours before stripping enough armor to make a difference. Of course if they can keep out of range of the tank while doing this, it might be a viable strategy...
It might also be important to rethink using open-ended rolls for damage. If the shots only do 10 damage on average but once in a while one does 1000 damage, sooner or later I'm going to lose my mech. One reason the Nethack wiki lists the possible kinds of instadeaths is that a good Nethack player can play a completely safe game: the know that there's no way that demon can do more than 60 damage before the player can teleport away, so there's no risk of dying. If there were a 1% risk of dying, well, you often fight more than a hundred demons... There's no need to make GearHead quite so controlled, since players can replace mecha, but a small chance of a serious outcome can make more difference than average damage. Zippy unarmored mecha are for gamblers - as log as you don't get hit they're great, but if you do, pow, it's kaput.
I think it's important to make sure that go-as-fast-as-possible isn't the winning strategy in nearly every case. (And that stopping doesn't immediately get you pasted.) Right now it makes you extremely hard to hit but costs only a little accuracy on your part. Why not make these penalties equal? You can build a zippy mech, but you'll have to get in close and use a high-BV weapon, a swarm of missiles, or an area-effect weapon to actually hit much of anything. If you want to snipe heads, you'd better stop and either take cover or be armored.
I think part of the problem is that space is too simple, tactically. There's no terrain features to take advantage of, so all you have control over is how far you are from the enemy and how fast you're moving. Formations might add some interesting tactical complexities; maybe an EW specialist with lots of INTERCEPT weapons could protect a group of automatic-weapons mecha and a missile carrier until they closed, then the missile carrier could unload all their heavy hitters and flee with the EW specialist while the grunts fight it out. This of course means you have to either control them all yourself (very annoying with the current UI) or be able to get the AI to act as a group.
