Doing full water changes makes it even more important that you test
your water. In fact, an uncycled tank requires more testing then a
cycled tank. You'll need to purchase test kits that read the ammonia
levels, pH, gh (general hardness) and kh (buffering capacity) for an
uncycled tank. Having nitrite and nitrate test kits are good too if you
ever plan to put him into a cycled tank

Just remember that dangerous toxins in the water have no color or smell
so even if your water is perfectly crystal clear it could still have
deadly levels of ammonia, chlorine, chloramines or heavy metals. You'll
need to test and condition your water to be sure he is safe from them.
You didn't say how often you do your 100% water changes but in a 3
litre vase you should be doing these water changes several times a
week. (2-4 times is probably needed but you won't know for sure until
you start testing)

Could you answer the other questions too. It'll help to figure out what
the actual cause is.

What water conditioners are you using? Are you using any?
How often and how much food are you feeding him? (overfeeding can cause
ammonia levels to raise very fast)
What is the temperature and are you using a heater to keep it stable?

By thew way, beef heart is great nutritious source of food that is
easily digestable for bettas. I'm glad to hear you're using it. You may
want to add in a second type of food too to make sure he's getting
everything he needs in his diet. (This is a seperate issue from the
spazzy thing) Maybe frozen bloodworms, daphnia, brine shrimp, black or
white worms, just to name a few.