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That is the thing @edscoble I am going to do the hinge clamps, block and saddle myself. They are doing purely the conversion for me. I ordered the conversion parts through Evan using my C2W voucher.
I have the M-fork, but I swapped out the bars for a stem adaptor and MTB riser bar some years back. (Photos back in this thread.) - now I am going to the new M-bar because I like it better, plus it means I can get rid of the adaptor too. I had new M-length cables fitted in February. So cable length is not a problem. Getting the stem adaptor off and the bars in is time consuming, I know it too me a while getting it in - but not all day. Then take off the brake lever, and mount new lever with shifter. Take SS tensioner off and replace with new derailer. Take current sprocket of wheel and fit the 2 new sprockets. Replace chain, get shifter working. If I wasn't a lazy sod, I would do it myself and just get them to fix the shifter. I might still do t.hat.
Having done that before, getting the shifter to work properly isn't difficult, the hard part is ensuring that we do have all the necessary part to make it work (inc. the right chain length, sprocket sizes, cables length), it just take time to ensure everything is fitted.
A Gold Service sound OTT but it kinda make sense because it's technically a groupset fitting! especially with the additional work of suspension block, clamp etc.
Can you claritfy by what you meant by the new handlebar? I know you're talking about the newer shape handlebar, but what were you changing from? this is the only complication I can think of as the stem is slightly taller on the newer Brompton with the newer handlebar (the old one have a slightly shorter stem, but a taller handlebar) thus the cable housing length may not be 100% the right length to enable it to fold perfectly.