i don't think the R34 will be noticeably laggier to be honest but the logistics of taking your turbo off and waiting for the turnaround might be an issue hence a blown R33 makes a lot of sense.
the hp difference at best is usually between 5-15kw at the top end depending on who has tried the different housings.
have you called GCG and ask if they will accept a deposit just in case they will.
just a thought, is the whine due to a manifold gasket leak? has this been checked because you may have a pristine R34 turbo which will be worth selling whole if this is the case.
when the turbo comes off it may be worth removing the manifold and replacing the studs as they usually snap over time anyway. more money but it might be worth asking the mechanic. there should be signs of a gasket leak if they inspect it.