Thanks for the replies.
My concern with E bidding an immediate 4H is the suit quality and the doubleton spade and the vul.
OTOH, opposite a partner opening a 15-17 NT, E has a hand I would bid to 4H with - and a strong NT is the hand I am placing partner with, and I can tolerate 5C if I have guessed wrong.
It might go wrong, partner might be 3145, but otherwise pretty much must have either 2 hearts or 6 clubs.
They certainly can't be 4144 !
I'm going to quote something from the Robson and Segal book that pertains to East's decision.
(from the chapter on t/o double after an overcall - there is an example of 1D-(3S) and holding both unbid suits - i.e. the hand type E doesn't hold in the above)
Quote
The rule of thumb on borderline offensive hands is: if you are going to be ‘tossing a coin’ when partner reopens with a double, it’s better to make a slight overbid and double yourself. If, on the other hand, you want to pick the strain opposite partner’s average offensive hand, it might well be right to make a slight underbid and pass.
In this case E has no problem at all should partner reopen - they want to play 4H.
Conversely they don't want to X and have partner bid 5D.
I think where this potentially falls down is Cyber's point about the opps bidding 4S.
I think that on most days 4H by E will work out best.
Keeps open slam options and also better positions the partnership should S extend the preempt, with only a small tail of disastrous outcomes.