So I replaced the original Garrard 401 mat with an EP

Vic at TransFi has an interesting new mat, one with little nubs the LP sits on, the LP suspended above the surface of the backing sheet the nubs are attached to. I don’t approve of that design (there are others making similar mats, primarily British), but some users like what they hear. Vic argues than any surface an LP is in direct contact with will cause reflections from that surface, not absorbing them as claimed.

I have the transfi mat and it makes the sound thin and bright

Since 1977 I have been using the Hiraoka Diskmat SE-22 on my Ariston RD11S (cost new was $20!). Tonearms and cartridges have come and gone - yet this Japanese mat remains! I regard it as a perfectly neutral device, neither adding nor subtracting from the overall sound of the Ariston + arm and mc cartridge. I bought it new from Harvey Sound (48st NYC) in '77. Never felt the need to change or upgrade, unlike my other components! For me, it's a keeper!

Did some back and forth and can confirm the result of removing the mat and replacing it with a 10" record:
1. Warmth - a slightly yellow-brown 'coloration' has been removed
2. Heaviness - with mat, it sounds like the musicians are behind a curtain and on a smaller stage
3. Brighter - As @pani said, it is definitely brighter - but much clearer. Rim of drum and plucked bass distinct, clear and fixed in space.
4. More air, depth, and dark space between instruments instead of a wall of warm sound - less lush. plucked strings snap into space in a startling manner. 
5. Increased pace - I had to test speed with strobe as I was sure it was running faster without heavier mat - it was exact.
6. Sounds louder - confirmed by others present.
Notes:
a. I can understand bright recordings being irritating but the improvement is too much to ignore.
b. I am convinced the mat damps and veils the sound. It's like going from Mullard to Telefunken.
c. Surface noise frequency spectrum shifted up slightly.