Betta may be dying??

You said big water change.. how big was the change?
How long had it been prior to the big water change did you do the last water change?
And if 50%+ how did you acclimate him to the new water chemistry.
And was his behavior before or after the big water change?

Size of the tank?
Normal water change routine/%?
Temp of the tank?
Tank mates?
Water conditioner?
Water parameters?

Other then his behavior, any physical signs of illness?

It could be any number of things, without more information other then his actions, can't help too much.

But at this point I would say it has something to do with the water change or something in the water that is not agreeing with him..

I would have to hazard a guess to why he was acting the way he was, was because you went too long without a water change.. much longer and you would of lost him.

The 60% was too big to do after that length of time, but if he is acting better then it didn't get to him too badly.

The algae eater will outgrow that tank (depending upon species, most will outgrow a 10 gallon), so keep an eye on it and in the future you may have to rehome him.

Nitrates still too high, even after a large water change.. the only thing I would suggest is a water conditioner, such as Prime, Tetra AquaSafe, etc.. even with well water sometimes you will still need water conditioner, especially if you become lax with the water changes. Nitrates under 25ppm is ideal (I believe up to 50ppm can be considered safe, but *may* cause long term health issues).
Go ahead and do a 10% water change now, and another day after tomorrow tomorrow to try to bring it down some- and use water conditioner. The water conditioner will also help with controlling ammonia.

Nitrate can be present in the aquarium as it usually is to a certain extent.. but excessive amounts usually means there is too much fish and/or plant waste- did you vacuum the tank when you did the water change? If not, then it's a must, as it should be done weekly to bi-weekly.

Your system may be going through a small shock and revamp of the cycle.. the fish had adjusted to the way the water was (even if it wasn't safe), and the large change just changed everything. So we want to get it stable, yet safely do it..

So basic run down- change 10% of the water every other day for the next 6 days- so 3 days total of water change.
Add in water conditioner to help lower the numbers and bring it back safe- add it in for each water change.
Siphon the gravel, even if you did it on the large change, do it again for the 10%s to make sure it's all cleaned out.
Test the water the day after a water change and see if the nitrates are 25ppm, or less.. if so then you don't need to do any more changes for that week, but if they continue to be too high then continue the water changes until it stabilizes.
Keep checking the parameters regularly over the next week, as your system may try to re-cycle itself and have spikes in ammonia and such.

This is assuming you have no live plants...?

In the future, for a 10 gallon, filtered, no live plants weekly 50% water change with siphoning is needed to keep it clean and healthy.
For a 10 gallon, filtered, live plants weekly 30% water change with one or two siphons per month.

Hope he gets better soon..