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You can run 620's with the stock boom. With 600 edge FBL blades I've run upwards of 2700 rpm but you end up eating main gears, pinions, and one-ways every flight. I usually like to keep the HS between 2500-2600 which will almost eat main gears, pinions, and one-ways, but won't. With 620's, I'm not entirely sure how the heli will perform at certain rpm ranges but if it were mine I would start between 2200-2300 and work my way up to something I like.
Keeping the 600se boom could make the helicopter to tail heavy but since your customer already has said boom and belt and batteries and I assume it balances fine, the blade change will not effect CG so it should be a non-issue.