In strictly theoretical terms - since it's important to remember Parliamentarism or Semi-Parliamentarism has never had the votes to ever be enacted -, I have grown to believe the single biggest flaw in such a model is that A. due to logistical issues you cannot have a truly large unicameral body (more than 15-20 would be nightmarish to handle and coordinate); but B. having a body of that size may have the effect of excessively empowering a very select group to the detriment of other players.
There are conceivable means of partly addressing that - allowing the PM or at the very least the Cabinet to be non MP's is a must, otherwise you'll encounter dysfunction right away -, but it is an issue to be taken into account. Also, though full PR would be interesting to see, it bears reminding Federalists have had a informal veto power whenever this is discussed due to the quorums required for reform, and there's always an insistence in the need for regionally-elected representatives (though I remember Yankee once suggested the German model - as opposed to a Westminster concept - seemed more "acceptable").
(All that side, good to see you back in the game!)
Perhaps the Prime Minister would have to belong to the Parliament, but the Cabinet could be non MPs?
It's not ideal, but you could also have each region be a multi-member constituency with 5 MPs? Or perhaps each region could elect 2-3 MPs, and the rest would be elected nationwide?