Is there a cost effective way to get my iPad repaired?

I sent my iPad for repair ...

Was that directly to Apple or through a reseller? If you sent directly to Apple, you would have received several emails regarding the status of the repair. iDevices that are Apple service replacements have a model number starting with "N.

[from Settings > General > About]

Does yours show the N?

I hardly used the replacement, maybe 15 to 20 times over the last two years. Recently, when I tried to use it, I discovered it was stuck in a restart loop.

Had the issue appeared as soon as your received the replacement iPad, I think you would have a case. However, with your finding it two years later, I doubt any manufacturer would honor a one-year warranty after two years regardless of how little the device was used.

For practical purposes, in lieu of repairing and returning your own iPad, Apple usually exchange the iPad for a renewed/refurbished iPad of the same model and specification. The cost of the exchange is the same as would otherwise be charged for repair. Unless you have benefit of an active AppleCare plan, an out-of-warranty repair while expensive will be somewhat less than the cost of a replacement iPad.

As for out-of-warranty repair costs, Apple offers a fixed-price price repair. You can verify eligibility and cost for your region/country here:

iPad Repair & Service - Apple Support

If you have an active AppleCare+ plan, the cost of repair is reduced to a small excess/deductible fee.

For warranty replacements, Apple will often exchange for a refurbished device - these being declared by Apple as being the equivalent of new.