Never sell occupied unless you’re losing money hand over fist. 

Usually in the case of a sale/purchase combo, you should usually negotiate a few days post-possession after selling your property to give you time to close/move to your next property. 

However due to limited interest I've dropped the price, and I'm approaching my bottom limit, in which I likely believe it'd be a better financial decision to sell (obviously contingent on the sell price).

ANd I have a bridge to sell you.. 

Sell or demo everything that doesn't align with your goals. 

This is something to take into consideration when buying a property but also when selling the property, especially if there will be a mortgage involved in the purchase or sale. 

I am going to wait until rates drop a decent amount and sell my former primary, which is now a rental, at a premium.

and who can you sell (or not sell) the property to?  

Ensure TaxAct is correctly reporting the adjustment on Schedule E and Schedule 1, Line 8, as IRS compliance requires.

If you anticipate selling the replacement property in a few years without another exchange, the tax deferral may only be temporary.This post does not create a CPA-Client relationship.