Personally, I do not think it's worth less time in each lodge to spend time at Bumthang in the spring/summer months. Punakha, Gangtey and Paro lodge are very special and deserve to be enjoyed thoroughly. I spent 18 days in Bhutan, visiting all lodges, and honestly, I felt like I could've spent even more time at Gangtey, Paro and Punakha.

So, if spending under two weeks, I recommend doing fewer properties with longer stays and enjoying them thoroughly.

Bumthang is sacred as it is the region where Buddhism took root in Bhutan. It is home to the oldest temples and some of the most significant festivals, like the Fire Ceremony, etc - which occurs in October-November. In my view, this is the main reason to visit this lodge.

May is a wonderful time with mild weather, blooming landscapes, and the chance to witness captivating weather for trekking and hikes.
Punakha, Gangtey, Paro and Thimpu are preferrable for this time period.

Gangtey valley is particularly glorious in May. Green and alive, blooming pink Himalayan rhododendron flowers and yellow wagtail along the trails.

Paro is one of my favorites, save this one for the end, so you are acclimatized for a Hike up to Tiger's nest.