Carb slides stuck

A good start would be to give everything an ultrasonic clean and see if it is still tight. The pilot chamber  will definitely need a clean out anyway.

Amal carbs, both Monobloc and Concentric are notorious for distorting  when the mounting studs have their nuts overtightened. This can affect both the O'ring mounting faces and the slides.

When I rebuilt mine which had been in the garage for many years, I thought these will be close to worn out and bought a set of new premier carbs.

I have wondered what is the mechanism that  bows carb flanges.  Certainly the nuts (or bolts on Rudges)  dont want to be tight.  Nylock nuts or nutlock  and an  O ring detail  seem to  reduce the issue. My  thinking is that heat with the attendant expansion  is the culprit  and the effect is magnified if tight fixings force the expansion  to that path.  Filing the flange flat is not the best answer and does nothing to correct  distorsion of the slide chamber. It is possible  to use  a jig and vice to correct all  the problems. A good thick heat insulating spacer  between manifold and head seems to fend off the issue but then  we have to think about  carb icing !.  A timed or thermostatic  electric element  as used on some bikes would be ideal.

Clean slides with wire brush, remove any bruising & emery slide with 600 grit approx. to smooth over score marks. Clean out slideways in carbs. the same. If slides still stiff, emery off high spots in the carbs, may have to use 240 grit for high spots. Slides should drop to the bottom on their own. Flange & float bowl surfaces can be flattened with a piece of 120 grit emery on a sheet of glass (window). Can be tedious. 

Don's suggestion is ingenious, but I worry about the possibility of the plastic bolster working loose — if this happens with the throttle wide open you potentially have a big problem.

My feeling is for the instant throttle response and smooth pull through the mid-range....If you want that then there are probably two choices  - Buy new Amal Premiers or get the existing carbs to Martyn Bratby.

Applying force to mazac castings is always fraught with danger.