Hi Charlie.
There are a number of frames currently available known as ottomans.
Usually faux suede or faux leather where the entire mattress lifts up by use of pistons enabling you to utilise the entire space in the frame.
This would be an ideal solution for you.

We have a range of ottoman bases that can be viewed here. We also have an article explaining everything you would need to know about ottomans here.

Hope this helps, John. 0161 437 4419