Hello kirsten,
given that the weather is so foul and hot at the moment- take super care when you do figure out how to move them that they don’t overheat in transit. Did you read my story about how I killed a hive a few months ago?
I thought I had done everything right. Turns out I was quite wrong. I would hate for you to have a similar bad experience…
If I had to move again under similar conditions I would consider either moving them at night- immediately after they are closed up after the bees return- or I would make a ventilated cover board/lid. Then I would move them absolutely first thing in the morning and do everything I can to keep them out of the heat and sunlight.
I think in my case the bees had already started to suffer during the night after I closed their entrance. It was a very warm evening- and I think if I hadn’t closed the entrance the bees would have been bearding and fanning at the entrance through the night. I stapled fly screen over the entrance so they would have ventilation but I think bees probably crowded that area and blocked the entrance. From there things spiraled out of control… 
I moved two hives- one was fine- the other was destroyed. The one that overheated was such a strong colony with so many bees trapped inside that they simply couldn’t cope.
I would be relatively easy to make a screened lid for the hives- and I think you really should consider doing it. At a pinch you could just staple fly screen over the top box and then move them without the lids/roofs on. Unless of course you have screened bottoms already? Although reading around I found a few stories of hives with screened bottoms over-heating in transit too.
as for actually moving them: is there way way you could induce some strapping individuals to help with carrying them?