Do you have a stock alternator that supports the red charge warning light on the dash?  If so, what is the charge warning light doing (key off, key on, key on with engine running)?

The slow starter and misfiring may be due to your battery and/or alternator.  A 5 year old battery may simply be past its prime.  An alternator that is not charging that battery consistently can also be to blame.  

The 123 distributor is electronic.  Others will have to tell you its limits but it will be expecting to see a full 12.5V supplied to power its electronics.  Reduced operating voltage can prevent electronic ignitions from working correctly.

Temporarily hook your multimeter between ground and the car's switched power (any dark green wire behind the dash).  Turn the meter on when you drive.  Take note of the voltage on the meter anytime the engine starts to misbehave.  Also, note the voltage while you are having trouble cranking the engine over.

Good morning

I'm having a weirdo problem with my 77 Mini. 1275, 123 distributor, high compression pistons, 44 carb and stage 1 kit. I did a complete tuneup, cap, rotor, wires and plugs, before I went on a 400 mile road trip last month. Trip went fine. Oh, I used a slightly colder plug from stock due to the bigger carb and higher compression. Don't really think I needed to but it said tuned road engines and I like the sound of that. 
Anyways, the other day I went to the gas station and when I went to leave the car acted like it had a weak battery and starter would spin at half speed. Took about 30 seconds to get it to fire. Drove it home and parked it. A week later (yesterday) it fired up like normal and I took it for a spin. I thought I could hear a slight tick as I was driving. Went to a friends house. 2 hours later when I went to leave it did the slow starter thing again. Finally got it going and when I was almost home it started making a noise like an extreme exhaust leak. I thought that maybe something in the exhaust had come loose. No, it was misfiring. Idling in the driveway I unplugged the plug wires 1 by 1 and when I unplugged  2 & 3 there was no change to the motor. 1 & 4 and the engine would sputter and almost die if you didn't reconnect it quickly. I took out the plugs and cleaned them and tried a different plug wire but no changes. 
I cleaned and relocated the engine ground wire. Still does the slow starter. 
My battery is 5 years old. 
Had it happen once where the alternator was dying and it would only partially charge the battery making the starter seem weak.
Could the electrical issues be related to 2 suddenly dead cylinders? 
Could it be possible to drop 2 cylinders at the same time? 
Is the 123 to blame? 
Can this post be any longer? 
Will driving on 2 cylinders give 2x MPG? 
Are the folks on this forum the cream of the Mini world?