I attended the open day at LBS last week, and managed to spend about 10 minutes with Tamsin, one of the admissions managers. I specifically asked her about R3 & 4 and the numbers, as expected she wouldn't provide figures - but did tell me that last year they accepted around 50 people from R4 & the waitlist. Someone even managed to get an admit a couple of weeks before the term started. She also confirmed (as did a couple of others I spoke to) that the bulk of apps come in R2, so there is potentially an advantage in applying to the other rounds, as the numbers are alot lower.
R3 is the deadline for scholarships etc, but I guess your not bothered about this. If this was your 1st attempt, I would resign myself to taking the test 2 more times max. My concern is that if set your heart on retaking the test with the intention of meeting 23rd feb, you will be putting yourself under too much pressure and will not be in a positive state of mind when you retake the exam. To mitigate this pressure I would stick to the plan of applying to R3, but resign yourself to the possibility of having to retake again and apply to R4.
You might find this hard to believe but I went from 640 to 750 without doing any extra work. The key for me was to not let the test psyche me out, I resigned myself to taking the test as many times as it took to nail the f*cker. I decided to obliterate the GMAT regardless of whether I was going to apply for an MBA, my defeat had become personal! With the pressure of performing on the test out of the way, I waltzed into the next test like a cowboy and strolled out like zorro (well i was actually shaking like a leaf at seeing 750 but nevermind
). Overcoming the phsycological aspect of the test had allowed me to overcome the test in entirety.
One caveat I should mention is that I am also applying to LBS for R3!