Backfire when hot

So im at a loss with what to try next, my cars a 83 1300 with weber 34 ich.
 Ive replaced ht leads plugs coil dizzy cap and coil, it has electronic ignition
 I booked it in at a classic garage and they set the carb up and it runs amazing ticks over lovely and starts easy, they also checked timing and said it fine.
 the issue is after 20 min of  faultless driving itll start bogging out when i push the acelerator pedal, and then start backfiring and jerking and cut out, it will re start run rough as anything bog and backfir but i can manage to limp it home, first thought was probly too rich when hot but ive changed the main jet down from 125 down to 120 and turned the mixture screw to 1.5 turns out. The fan kicks in and temp gauge only ever gets up to below half way. 
Any ideas? 

Do 1300's have an ignition amplifier? My 1800 DX does and had the same symptoms you describe. 

The amplifier on mine is located in the scuttle area by the blower. 

Have a look to see if you do. Could be work considering, when mine was changed it was sorted. 

Ok ill have a look thanks 

No 1300s dont have one of them, went a run last night and it started doing it before it got fully hot, really cant think what it could be

Huummm,
Another thought just came to mind. I had a 'miss' on mine a couple of years ago. Got so bad I booked it into the garage to get sorted. 

On the way it started again, then conked out totally. Turned out to be the alternator to battery lead had rubbed through and was intermittently causing a short. 

A heart pounding few minutes when I popped the bonnet!! 😳 Managed to get a couple of snaps for the insurance company just in case it really got going - it didn't thankfully!! 🥵