Times of year when crowd in Makkah/Haram is at its minimum?

Yes. After Ramadan, the rush drops a bit but you can't say it to be at the minimum.

The current ongoing expansion project will go till 2020; and before that I don't think we'll ever see the no-rush times as we did a few years back.

Yes, you can expect a few off-peak days after the local Eid holidays, when the schools/universities re-open. Even better if you go late at night.

If you have elderly people with you, take advantage of the new Tawaf circle, above the ground. They only allow elderly/wheelchairs + one person to accompany them. Sa'ee is usually smooth-flowing even during Ramadan.

If you plan your trip any time 2 weeks after Ramadan, you will find the next three weeks are relatively quiet and a good time for elders to visit.

The other quiet time which you have correctly identified is after Hajj (around about 15 Muharram to 1st Rabi Awal - a 6 week period) where it will also be quiet ...during these 6 weeks, avoid the week where Saudi schools are on holiday)

Thanks a lot for your replies people...

the absolutely most minimum number of pilgrims is after Hajj, around 15th to 30th Muharram

Hello fellows. I performed Umrah last weekend ALHAMDULILAH and based upon my personal and recent experience there are no such days where you didnt face crowd .but for my opinion these days are perfect if you are performing umrah with elders and even by your self you can judge the crowd like I performed tawaf-e-widah before Duhr salah in just 20 or 25 mins all 7 rounds (By the way i walk little bit fast )and Alhamdulilah got sitting in 2nd row in front of Bayt ULLLAH for salah. I believe only one obstacle may be faced by elder persons is cold weather but as every body know Cold in Makkah is very pleasant and bearable unlike Riyadh. So in Nut shell these days in year are good to go. Remember to keep us in your prayers. JazakaALLAH Khair .