Some things to consider that may help you decide what to do:
a) You are presently on the BTYahoo email system and you will stay on the Yahoo platform with all the possible problems that come with it. Look through the forum to see some of the issues that some users have been having.
b) If at any point, although this looks very unlikely you do get migrated on to the BTMail system it does not let you set up new disposable addresses. When the initial migration took place any current disposable addresses were migrated but I would not depend on that happening if the migration ever re-started.
c) If you use a non ISP email supplier such as gmail you will not be dependant on your ISP for your email and this "frees" you up to move ISP with out worrying about what happens to your email account when you move.
d) If you can not have your disposable email addresses associated with your "new" email account you could take out a BT Premium email subscription for £5 per month until you move to a new email supplier. The subscription is on a 30 day rolling period so you can stop it with 30 days notice once you have moved across to your new supplier.
I've found BT to be a good provider generally, (both voice & ISP), but they seem to have taken their eye off the ball with email. I have already suffered some of the irritating "Yahoo" quirks that you speak of and the new BT mail feels like a backward step. It is useful to note the 30 day BT Premium mail - I had assumed 12 months - even so, I feel the need to jump ship and there is no point in hanging about.
(a) In the next few days, I will create a new parallel email structure with a non-ISP as you suggest. You have reinforced my view of the freedom that brings, thank you. I'm looking at gmail right now, who also offer aliases and "appear" to have decent reviews.
(b) I will also keep my BTYahoo email addresses and associate these with the new BT Mail based account in due course. Given the cautions on here, I don't have a lot of confidence this will do all that I want, but it might provide a safety net for any incoming emails overlooked in my new arrangement.
As a bonus, there are few posts on here (if any?) about associating the 2 email systems, so later I will post back my experiences and hopefully fill in any details of the way it works or not. (Whilst fully acknowledging the obvious expertise of contributors to this thread)
As and when, I'll gratefully accept the offer from the mods to arrange the association.