Well, you have a camera - a smoother one than a Kiev or pre-war Contax, too!
Get the IIIa cleaned and forget the meter - it can probably be revived for a price in the same range as a Contax/LTM adapter or the amount you have to spend to get a good Kiev (which usually takes three attempts).
That is, a mere cleaning will generally address Contax shutter slowness. Only the fastest speed may still be unreliable or lost - if the widespread 1/1250s capping issues don't magically heal themselves in the CLA (or after some time of intensive use), they can only be repaired by taking the entire shutter drum apart, a risky repair effort (the part is press fit and was supposed to be replaced as a whole) probably above the camera's worth.