Hi mtrvl and welcome to the Forum!
There have been several threads here on the Semi-Autos section about recoil springs, including the dual nested springs that fit your 4516 no dash, which are the same ones that fit several other .45 autos in the 4500 series. Yes, finding replacement parts has been challenging recently for a number of reasons. Not to worry though; a fix is in the works, and if you can hold out for a few weeks, a new manufacturer's springs (as fabricated from a pair of new S&W springs we sent him) will be available and will be extremely good quality.
Keep watching this space, and in the meantime, you might want to check out the thread by BMCM about us "being on our own" for replacement parts.
If your pistol is down until you can find a pair (or either of the springs) let me know and I'll be glad to send you a pair that is still in good shape but that I replaced in my Shorty 45 recently. They (or it) should tide you over until new springs are available.