I use small base dies and I only shoot 5.56 in an AR style rifle. No problems with them here either. I use LC brass and CCI military primers only btw. There CAN be a problem with bullet setback if you don't use some kind of crimp, depending on the rifle, etc. I've noticed it with mine, and I have a several 77gr. SMK's and Hornady 75gr. T1's that have to be pulled and reloaded due to no crimp and setback issues. I've switched to the 77gr. SMK's with the cannelure, and I've had no problems since. Accuracy is about the same. I also use a Lee Factory Crimp Die. In fact, I have one of those for every round I load for, and it's the only Lee product I use. These things work really great. Note: military Mk262 mod. 0 had no cannelure, and then they came out with the mod. 1 and it has the cannelure. Obviously they ran into a problem with setback too.
As for powder, it's been dried up, but there's a thread on here mentioning some dealers. In addition, I looked at Ramshot's dealer/distributor sites and started looking those up. No TAC powder (IMPOSSIBLE TO FIND!) but these big internet dealers get lots of other powder in from time to time but it goes FAST. I just got 10lbs. of H335 and 10lbs. of BL-C(2) shipped, but if you order online make sure to buy a lot due to the hazmat fees. I should have gotten that can of US869 while I had the chance. Oh well. Next time. Anyway, shop around, some have this in stock but not that, so you have to find "just the right place" to order from to take advantage of hazmat. They also have limits, some are harsh, others not. Expect to buy in only 1lb. cans regardless, save .50BMG powders in 8lbs.
I understand H335 is a better, more standardized version of the military powder used in the M855. So you can load 62gr. SS109's to practically the same as the M855. Note: Factory M855 is actually hotter than what you'll find load data for, in general. However, load data does show this powder as offering maximum velocity compared to other powders, so it may be the best for loading M855 clones.
BL-C(2) is a better, more standardized version of the military powder used in 7.62, and what they use for (I think) the Mk262 with the 77gr. SMK. According to my Hodgdon data, it shows the BL-C(2) as offering the highest velocity for this bullet @ 2804fps., so why not use it anyway? Sierra shows TAC @ 2750fps. followed by AA2520 @ 2700fps. FWIW, BL-C(2) also evenly compares to AA2520 in my 6.5Grendel with 120gr. Nosler BT's.
These two powders, H335 and BL-C(2), can get you by quite nicely, particularly for the time being if nothing else. There are bulk military grade powders similar to these available, but they generally aren't as standardized as the commercial powders are, and it's likely from pulled ammo. In short, I prefer the numbered, commercial grade powder.
For 69gr., highest velocity is obtained from AA2520 @ 2900fps. with Varget next @ 2850fps. (25.3gr. Varget @ 2750fps for best accuracy according to Sierra). Hodgdon shows Varget as the highest velocity @ 3024 followed by BL-C(2) @ 2954fps.
For 55gr., Sierra shows XMR-2015, X-Terminator, AA2230, Viht N135 and TAC as offering the highest velocities, ~3100fps, followed by Viht N130 and IMR-4198 @ 3050fps. H335 next @ 3000fps. Hodgdon claims 3203fps though. These discrepancies in velocities likely have to do with the test barrels Sierra used vs. Hodgdon.
There were several other good powders for the 55gr. in the 3000fps. range as well according to Sierra's data. Also, from personal experience, 55gr. bullets don't perform nearly as well out of 1/7 twist barrels. 62gr. is about as low as I'd go with a 1/7 personally, but the 77gr. SMK's work really nice.
I got all this data and information from Loadbooks, which is a compilation of data from several bullet and powder makers, copied and put into one caliber specific loading manual. I highly recommend these, if available, for every round you load. Make sure to look online to see if the load you want to use has been modified, as some of the data is a little dated, depending. But instead of purchasing several books full of load data you'll never use, you can get these for ~$5 ea. and have all the data you need for that specific caliber. GREAT investment, IMO.
Merry Christmas and good luck and safe loading!