From my experience there is no need to clean between lube changes (different brands), here is what I do:
-New rifle: clean the bore with a quality solvent (I like Kroil, TM, or Butches), then dry the bore & chamber very good!
*when cleaning use a bore guide, a quality rod like a Dewey coated rod or similar, and lately I have been using the VFG felts for rimfire and really like them:
http://www.champchoice.com/store/Main.aspx?p=CategoryBody&c=CLCRVF
-start with ammo #1 and it can take 15-20 (sometimes more) to season a freshly cleaned barrel, but on a good quality properly chambered barrel normally 15 or so it will settle down, shoot that until you are satisfied that you know how it shoots
-change to ammo #2 and your first 3-7 rounds will more times than not be super accurate, don't get excited this is not what to expect, it is just an anomaly I see in very good shooting rifles when changing lubes. The next 5- 10 rounds will start to scatter a bit but after 10-15 rounds with the new ammo it will be settled down and shooting consistent.
-continue this cycle with all your ammo and you will see the trends that your rifle has, but I bet it will be very similar to what I just outlined above, personally I don't waste time cleaning or dry patching b/c you will have to shoot at least the same or more rounds to season if you clean, a dry patch may save you 5 or so rounds but that is not a guarantee, I use the fouling rounds to confirm my position and work on the basic mechanics of building a position.
One other thing to note some rimfire barrels (more specifically chambers) may need to brake in a bit depending on how clean the chambering job was done. This can take much longer than with a CF as to be expected with less pressure and softer bullets, so if your accuracy isn't what you expect for the first 50-100 rounds be patient and give it a few hundred more paying attention to accuracy trends. There is no need to do any sort of 1 shot and clean method for "brake in". However if your accuracy isn't as expected and your approaching 100 rounds or so give the bore a good cleaning, b/c if the throat is a little rough it at be stripping some lead and accumulating in the bore.
Lastly do not forget about what a huge effect atmospherics has on rimfire, a 1-2 mph full value wind at 50 yards is worth around 0.100" in POI shift (about 1/2 of bullet diameter). Temperature is also a big consideration, I see accuracy start to degrade around 45f-50f, from 30f-45f it can significantly be affected, and in the 20's and below it can be total crap.
These are just my thoughts on the subject, I am no expert and I don't claim this it the only method.