It's hard to see exactly what is wrong from the pictures, but I'll take a stab from what you describe.

You say the mast base has sunk 3/16". If the base is "sinking" into the deck of the boat, then the plywood core in the laminate under the base is rotten. This is a fairly common Express 27 malady. This needs to be fixed--the sooner it is fixed the less extensive the repair will be.

If this is the case then it would describe your rig tuning problems, as if the mast base is angled significantly then it could impart the inverted bend you are describing. This is no good, and could possibly lead to rig failure--more likely it will just be impossible to tune your rig well.

The core under the mast is plywood, which isn't really great at withstanding rot. Especially in the mast base area (lots of holes that invariably leak). Fresh water and freeze/thaw cycles are especially bad, but the problem is common in saltwater environments also. There is no alternative but to cut out all the rotten core and rebuild the deck in this area.

The good news is that if the interior is intact (main bulkhead, main bulkhead supports, and inner skin) then the repair is straightforward. Just cut and grind away a good sized area from above, replace the core, and then the skin on top.

I recommend a repair area at least 18" square--I've seen some small (mast base sized) repairs that "punched through" the inner skin at the edge of the repair. G-10 (multipurpose garolite) can be used as a replacement core that will never rot or crush no matter what you do to it. The hard edges of the G-10 need to be dealt with (tapered, reinforced skin) or they can cause cracking.

Unfortunately this is a repair that is worth putting on the short list. You may be able to get a couple careful sails in, but this will probably only get worse and having your mast invertered is not a good thing.

If this isn't your problem, then I can take a stab at rig tuning...