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I can't compare exact apples-to-apples - but I have done pretty much the same as you. I have the CSR, then got the CFU, then got the Ink Unlimited, then got the Freedom. All in less than a year.
However, both the Ink and Freedom came with starter limits. I think this was due to having too much available credit on the CSR ($28.5k) and CFU ($23.5K) - so don't be discouraged if the lines start out small. I ended up moving $4k from my CSR to my Freedom. I may move $8k from the CFU to the Ink.
You look to be in good standing to get approved without any issue. Yes you will still be eligible for the signup bonus and yes you can move UR from the INK to your CSR (I know you didn't ask either of these, just FYI)