I just realized this is a 2 year old post but if it hasnt been built yet,
all the above plus a heads up that unless the donor 15 is a snub the 4" Model 15 -3 has a frame that is chamfered at the corners where it meets the barrel rib,
(Same as center gun below)
Shown L to R are the pre war K22, early post war K22 (same as Model 18/15 ) and later Model 17 .
The Model 17 used a slightly wider barrel rib starting in 1955 that will not mate to your 15-3 frame cosmetically.
Other options are to either find an older 6" narrow rib K-22 barrel (1947 - 1954)
or to use a Model 14 frame or a Model 15 frame that is dash 5 or higher as a donor.
Also if you use a full underlug barrel you will need to use a Model 19 frame
or a Model 15 or 14 that is dash 6 or higher Otherwise the ejector rod shroud will overhang the frame.