I have a heat pump hot water tank. Some things to consider:
1) the heat pump will pull heat from your basement. It will take the air temp down a few degrees. If you have any living space down there, accommodate for that.
2) it can pull moisture from the air. Usually a good thing in a basement!
3) they don’t need vented, but they do need to have a condensate line run from them. The water from your clothes and from transferring heat needs to go somewhere. You need to either pipe it to a floor drain, to a sump pit, or pump it up to your dwv plumbing.
You may want to try cleaning your current dryer inside, lint trap, exhaust hose, and the exit point from the property before buying a new one. Lint, dust, dirt, rust, etc can all reduce your dryer’s ability to dry and increase run times.
I would take option D. Clean your dryer, see if that helps. Heat pump dryer would be my last option, given the costs, unless the “negatives” are actually positive side effects for you. Then it may be worth considering. But man, they are pricey here. A new electric dryer can be had under $300. A used one on Facebook or Craigslist? Under 100. Like someone said upthread, the electricity to heat conversion is as close to 100% efficient as you can get. A new one doesn’t necessarily mean it’s going to save you a ton of money.
Gas, while it can be cheaper (and I like heating with gas way more than electricity) also comes with side effects. You need to plumb a new line in, and it does create carbon monoxide during combustion. You have to be more diligent about making sure it exhausts correctly.
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