Stick to India and enjoy.
We did the road to Ladakh and Leh via Kashmir in 2009. When we were in Manali in April waiting for the road to open we had several differing reports from local police and tour operators about when the road would open, some said a week some said longer. After almost 10 days we decided to go around via Kashmir and Srinigar to Leh. By the time (approx 10 days later) we got to Leh in late april (only 2days after the road opened up) we were pretty much the first tourists in Leh. We had the whole place for ourselves and really enjoyed it. However I can understand that it wouldn't be so enjoyable in July and August when the hoards of tourists arrive from Manali, by plane and via Kashmir.
There are several tour operators that do the whole loop including Kashmir, Ladakh and himachal pradesh in just 2 weeks on enfields, so I don't think you'll have a problem with that choice of bike. And I don't think you'll have a problem with that time of year either. That said it is the Himalayas and mountains are unpredictable at the best of times and that needs to be respected. Unfortunately you must share the roads with less educated people and it can be dangerous so keep your wits about you.
Back in 2009 the Spiti road was closed due to avalanches and it couldn't be driven all the way and there was a need for permits. Although we would like to have gone, time wasn't on my side. I would suggest to you to keep a few days up your sleeve just in case it takes longer than expected to get a permit or there is an avalanche blocking the road. I think you should concentrate on enjoying the one area rather than spreading your time to thinly and attempting to fit in a tour of Nepal. Nepal IMHO deserves 1 month alone, 2 weeks riding and 2 weeks trekking.
Btw don't hang around in Shimla too long, it's nice for a  or two but it is the Indian tourist destination for all those well-to-do indians wanting to escape the Delhi summer inferno. And as we found out their is a fair share of crime and we had some bags stolen and our bikes tampered with, even when parked in the hotel parking!
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