How are you measuring the humidity and at what temperature? Buy a decent hygrometer. The digital read out on a Frigidaire dehumidifier is very inaccurate.

The $200 dehumidifiers you buy in big box stores don't work very well. If you want to go from 70% down to 45% in a basement then you need to buy a better dehumidifier. Here is a link to Santa Fe dehumidifiers. They are a lot more money but they do a much better job of removing their rated moisture.

Years ago I was faced with a similar issue in my basement. I got rid of the dehumidifier and installed a pricey casement window A/C... yes, cooled a little. Yes, brought down the humidity drastically.

The problem, as you have discovered, is humidifiers put out a lot of heat. You need to duct that heat out of the basement. Get a dehumidifier that has an exhaust duct. Alternatively, send more air from the main AC system down to the basement.

I'd echo the point above about checking the humidity with a decent hygrometer; I use a modestly priced dehumidifier from time to time and its display is way off compared to any other humidity gauge.

Anything unusual about the house? Is it new? Do your neighbours have similar problems? (Is there a source of water that's keeping it so damp?) Obviously worth seeing if the A/C operation can be tweaked to get the humidity down.

While it may be overkill, a dehumidifier that can reject the heat outside ... is basically an air conditioner. While it would be a bit more expensive, installing a minisplit might be worth considering. Would also provide supplemental heat and cooling. And cheaper than dealing with the unpleasant results of high humidity in a basement. If you use the finished basement a lot, I wouldn't rule it out.

Instead of a minisplit in a basement, a much cheaper window A/C might be cheaper and more effective. The temperature swing is typically not a big deal in a subterranean basement - the effect on humidity can be drastic.