It indeed couldnt hurt to ask your LFS for leftover packaging boxes. Those things are great, but you should still bag the fish like @ombomb said.
Ive tried this and had success before... it could work for you because your tanks are similar n size (I had two 60cm tanks). They were both well planted and needed moving, so I bagged the fish and put them in a bucket for transport. The tanks however had sand substrate and were planted, and had been planted for a long time so all the roots were all over the place and tangled into eachother. Unlanting the tank would have killed the plans, so I drained the tank until there was only a 1 cm layer of water only just above the sand. Then I got some polystyrene sheets from B&Q - theyre used for insulation - and I cut one so that it would fit right down inside the tank. Worked like a charm! It kept the water in and didnt kill the plants (which had all fallen over of course).
The best bit was that I used the rest of the insulation sheeting to tape to the corners and base of the tank (now light enough to lift with a bit of effort) so they were really well protected while moving