So I asked the seller of the £108 tent if they had a storage bag, and they said no. I asked the same to the £118 tent seller and they said yes. Additionally, this tent has extra vents that may prove useful (circled red). While this tent also has unnecessary doors, the borders are silver lined so they're not as easy to see as the black borders of the £108 tent.

I found out that there is a pop-up grow tent, but it doesn't seem to address the fabric manipulation issue and, at 2.2m, is too tall to install. I don't have that large, white pocket dimension the people in the video below has.

There are tents for bikes on AliExpress. The height isn't the greatest, usually coming in at 1.65m and this is a semi-circle, so the average height is much less. Most of them are 2 x 0.8m, but I have found a 2.1 x 1.5m one that looks quite nice inside:

https://www.aliexpress.com/item/1005004113699077.html

However, I think the dimension are actually for 1 segment and they're just showing that they're modular. I'd otherwise find it hard to believe that those 3 segments are 2.1m long.

There is also a promising looking tent that is 2 x 1 x 1.9m tall and is more rectangular:

Anyway, I've bought the Seuna tent. If that fails, I know a solution using grow tents does not exist and that any further research would be looking for something to use in April (because of AliExpress shipping times)  or some indefinite time afterwards.

There's also a cool looking tent that unfortunately has no floor, is a 1.8m cube that likely wont fit and usually costs £200 shipping included (but the listing below has some outlier shipping price)

This tent also has windows, which might be problematic or it might be possible to mount LCD backlight panels on the outside to give the illusion that the tent exists in the white pocket dimension.