Strelitzia and Agapanthus does not flower

A couple of years ago I purchased a bare-rooted Strelitzia plant in Madeira, and duly planted it in a planter, which sits outside in the summer, and in an unheated conservatory ( frost free) in the winter. It appears very healthy - no pests or obvious blemishes, and moderate leaf growth but so far it has refused to produce a flowering stem. The original stem was cut off at about 9" above the ground when I aquired it, and this is still stiff and green but is not growing at all. Should I cut this off altogether to try to encourage a new shoot to form?
As it is quite obviously not dead, I have no intention of throwing it out, and I feel that I only need to give it a little boost and it will be fine. The planter is fairly shallow, and I had thought to plant it deeper.
I also aquired at the same time a pair of Agapanthus plants ( species unknown ) and I am having similar problems with them. Now I know that Agapanthus benefits from being crowded so I have created a pot-bound situation for them, and now the tips of the leaves are beginning to look a bit anaemic. As it is unseasonably cold here at the moment they still reside indoors - and I don't expect any progress until they are outside in the better weather. Any ideas?

 

I grow mine in standard pots, but i think they would do better in deeper pots, if you change the pot leave it alone for a few years to get pot bound, thats when it should flower again.
For the Agapanthus, again, root restriction and they will flower.

 

Both are sun-loving, grown in the open in hot climates.

 

Thanks. Some Agapanthus species are hardy in the UK, but both the tender Agapanthus and Strelitzia are grown indoors succesfully(albeit not by me) and do flower if put outside in a sunny spot in a hot high summer - allegedly ! Most South African plants are growable in the UK - as they are not noted for requiring high humidity. Certainly the all year round weather in Madeira is not so much different to the high summer temperature here. I think this might be a case of wait and see but I will try a deeper pot for the strelitzia.
Thanks again
Malcolm