I'd agree that the height is a problem. I tried to grow three toms in
a 5' plastic greenhouse thing last year and it was a disaster for a
number of reasons:

- toms can get really tall, and the more you pinch them out the more
determined they get.
- the growhouse couldn't be ventilated properly without wind damage to
plants and growhouse.
- the amount of airflow around the fruit is poor, leading to rots and
other nasties.

Tomato plants are way bigger than you expect them to be. Pop them
outside somewhere sunny when the frosts have gone and you'll have a
hedge by August! Oh, and wear gloves when you're trimming them - the
sap smells and sticks to everything!

Good luck!