Perhaps the solution is more on the bioengineering side of things: make smaller people so they can fit in smaller rooms.
The trips themselves of course consist on transmitting the mind to be downloaded on a new body on the other side.
And you're a mind running on a computer! You were already going to experience the heat death! This is just a scheme to get the most subjective time out of it as possible. (Running slower is more efficient.)
Bay Area, 2020s: "Soon we will have rooms the size of a single computer"
OTOH can the heart perform equally good if human get miniaturized?