I like this idea. Would it be possible to go the extra mile and make it a truly game-changing feature by treating these beached LST's as mobile vehicle bases?
I haven't thought it out completely (so please be gentle), but if technically possible (code-wise), wouldn't beaching an LST with the ability to offload a dozen or a score of GVs (with troop and supply capability too), allow for some interesting fights. Right now, the GV spawns are well-known. If an LST group could be brought into an enemy's back yard at points that are not known, it seems to me it would add several fun elements (suprise invasions, new ships, new tactics). There might be more reliance on reconnaissance and coastal patrol, for instance.
The GV, and mission and capture- oriented folk would get a new way of attacking (heck, invading...), and the furballers and attack people will have a blast (literally) trying to take out the LST group and its air cover.
I think this idea above may have some holes in it, true, but maybe it's doable. If so, you could expect some hellacious combat as a result. Certainly what the OPs have suggested seems doable, even if it's not taken as far the above.
FWIW,