I will start off with setting expectations, in case yours are similar to what mine were....There are FAR fewer options for 22lr AR uppers than one would expect, given popularity of the platform and popularity of the cartridge. With that, the market is NOT under the same competitive pressure as others and the uppers are quite pricey, unfortunately.
That being said, the 22lr upper can be financially justified (if you need it to be) depending on the purpose. For me, I had joined a gun club, purchased a bunch of steel targets and really got into the craft of shooting--previously, I was only a casual shooter and expert gun fondler. As a result, I was spending substantial amounts of money on ammunition (even after selling my soul to Russian steel cased brands) shooting ~500 rounds per week of predominantly 9mm and 223/556. It was clear, I needed 22lr conversions for my go-to proficiency training weapons to maintain this momentum. Id say for 90% of drills recoil and report are negligible parameters, and instead repetition, sight alignment, trigger control, muscle memory, heart rate, moving/dynamics, and myriad other variables are the skills needing to be honed for high performance shooting. In that regard, 22lr was the perfect training caliber and enabled me to become proficient in those skills at .04$ per round. I shot MORE and spent less. For my set up (both Glock conversion AND AR upper), I believe my financial breakeven point was at ~3k rounds of ammo. The 22s literally paid for themselves in a month.
However, sounds like you want to build one simply to fill a void in the collection. And believe me I'm nearly air tight, literally creating voids at the most granular level to justify certain purchases, but just know if you are not building it to SUBSTITUTE high volume shooting of another caliber, it may get pricey, with one exception (that I know of anyway). That exception is '22modsforall' dot com. I tried to purchase a 9in 22lr upper from them but they wouldn't sell it to me because of the disgusting location I lived in (despite being legal--can explain if needed--its as convoluted as you would expect). I think the price was ~$200 buck and it came with 2 mags, linear compensator and BCG. I have no clue how reliable or the quality, but for $200, id be willing to do some Dremel work to get it running 100% if needed. I may even buy another upper just to try one of theirs out now that I live in good ol' NC
For my AR...
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The Upper: Tactical Solutions Kestrel
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@ muzzle: Spikes Tactical Barking Spider Linear compensator
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RDS Optic: Sight Mark Ultra Shot Plus QD reflex sight
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BUIS: generic made in china ALUMINUM (never get generic polymer from china, worse than useless). Drilled it for putting in fiber optic wire (forget the gauge off hand).
Some pictures below on my Troy Ind. lower. if any questions happy to assist.