. . . and was going to use BR4 primers but may go with Federal 205M if they are the best in this case. . . .
I *think* you mean you're going to test primers, and that is a good idea. I've found (one person, so small sample size) that different barrels, not to mention different powders, can show some serious preferences for different primers.
I spent the first 15 years of my BR life believing if it went bang, all was well, primer wise. Then a few interesting experiences -- same chambering, bullets & powder, but different barrel -- showed me primers are "an integral part of the system." YMMV.
I'd try the Russian primers -- Wolf -- because they are quite mild (and cheap). Since you've got BR4's, by all means test them, too. Another mild primer. But I'd also try a few hotties, either the Remingtons or CCI Small Rifle magnums. Odds are they won't work as well, but I have had barrels when the hotter primers shot better.
Shoot a 10 shot group with each (unless fewer shots let you rule it out), call your shots, and look at both group size and any unexpected flyers, where "flyer" isn't so far out of the group, but far enough to make you wonder.
As to the Hodgdon Extreme powders, well, all powders have some temperature sensitivity at the level we shoot in benchrest. It's a matter of degree. If you can establish and shoot in the middle of a "tune window" where that window is fairly broad, you may not have to change your load at all during a match. On the other hand, if for whatever reason it isn't broad, you probably will.
Next, get several types of bullets. Turns out that different barrels will probably show a preference for different bullets. Bullets are cheaper than barrels. It's not a waste. They don't eat much, and if one barrel doesn't like a particular bullet, the next barrel might.
Most .22s match bullets seem to be 7-caliber tangent ogive, but if you can find a boat-tail, it would be worth a try. Lester Bruno makes them periodically. Also bullets have different diameters -- "fatties" can sometimes make a difference.
Finally, you need to do this testing with as few rounds as possible. 3 or 4-shot groups will let you rule things out quickly. When you get to a promising point, then shoot the 5-shot groups.
Finally (a second finally), if you're new to benchrest, get a good book or two or three. Trying to cover larger topics on an internet forum is perilous. By all accounts, Mike Rattigan's book is worth having, as is Tony Boyer's. While perhaps a bit dated, Glenn Newick's book is well worth reading.
Hope this helps.