The problem with TOS is that there is no universal symptom complex and from the description you've given its possible that TOS is one of many different (but related)problems you have.
IMHO I would make the following points though its not a substitute for your own docs advice

1.If they noticed an irregular pulse but did an EKG straight away and it was ok then its probably not much to worry about, just ectopics or something. Esp if the 24 hour EKG was ok and you're not symptomatic. Do you have any regurgitation associated with your MVP? Did they say your pulse was still irregular or resolved by the time they slapped the EKG leads on ?
2. Even though the vascular surgeon said your blood supply was ok in your arm it doesn't rule out TOS as much of the vascular problems are positional.Also some of the vascular symptoms you're getting could theoretocally be irritation of the sympathetic nervous supply that can occur in TOS which wouldn't show up with a doppler
3.The pain you describe, is it in the region of the levator scapulae muscle? Its a common place to get pain in TOS especially if you have a tendency for head forwards posture. Do you have any increased upper thoracic kyphosis or difficulties with scapular stabilization on exam?
4. Your MRI doesn't show any nerve compression so theoretically the pains in your arm could be related to TOS. Its difficult to differentiate between radicular pain from the neck or TOS in you I think !
5.Why are you having a rheumatological workup ? Do you have joint pains/swelling/skin changes anywhere else ? Are they thinking your vascular symproms are Raynauds and ruling out an associated connective tissue disorder ? Is there any other reason your necks in this sort of condition eg.long term poor posture,weight gain,previous trauma,age, family history