There's some really nice stuff in here, both from the OP and from Taro. My thoughts:
1) I'd favour larger tiles over smaller tiles generally, as I'm assuming there are more people with larger screens than smaller screens. If we can also get the category filters and/or a free text filter, then the larger tiles have relatively little drawback, as you're not so likely to be looking at a full list of all of your mechs
2) In keeping with the larger tiles, I think I'd prefer something more along the lines of sabujo's icon layout, but I'd probably eliminate some of the info. I think a simple 3-state icon for weapons/tonnage (e.g. red for "empty/invalid layout", yellow for "not all tonnage used" and green for "valid, all tonnage used") is enough info rather than trying to convey the number of weapons installed etc. That then leaves a little more room for the engine display (great!) and icons for each installed module.
3) I don't know how complicated it would be to implement context menus for the UI (right-click menus) but if they were to do that, it could allow a rich set of interactions from the mechlab list screen without having to clutter up the mech tiles with buttons.
Imagine a right click menu that had these options:
"Configure" (there could still be a small config button, or it could be made a double-click interaction with the tile)
"Strip weapons"
"Strip Engine"
"Strip Modules"
"Strip Armour"
"Strip ALL"
"Add to List..." (if custom mech lists were implemented).
For me personally, that would save a *lot* of time when moving expensive items (engines, modules, certain weapons) from mech to mech. YMMV