delta 3200 is actually a low contrast film designed for pushing with a speed increasing developer resulting in normal contrast.
If you are using Microphen stock as per ilfords recommended dilutions with microphen, then shoot at 3200 and you will get a normal contrast index negative with ample shadow detail (an 8 stop range). However, D3200 and Microphen combination will be quite grainy which may or may not be what you want.
But you say you are using D76 and that is at least a stop slower than microphen with D3200.
Ilford work out ISO using ID11 (same as D76 near enough) so that speed of 1000 or 1250 will be about right with D76.
But if you must have the speed of 3200 or 6400 then microphen will be your best option, optimally at EI 3200.
Sorry, I need to elaborate here. My advice on speed alteration is intended to give the user an indication of shadow detail which is only marginally affected by development times. I'd use the time for 3200 which may blow the highlights a little for the slowest speed but given that most users agree as has been stated by Allen that the next higher film speed dev time should be used because D3200 is a low contrast film then even the dev time for 3200 will only increase highlight density a little.
If 1250 to 1600 turns out to give the required shadow detail then the time for 3200 will be close to the right time
I think that Allen has got it right but the OP may need to discover for himself. Unless he experiments he will never know for himself what his right speed is.
The alternative is 9 shots at 800 then 9 at 1250 etc and cutting the film in the dark into four sections and developing separately and with knowledge of leader measurement to frame one and markers on a bench for nine frames this kind of cutting is possible with the loss of one frame at each cut but it is quite an ordeal unless the OP is familiar with and has had experience with such a procedure in the dark.
Of course Ilford recommends their own developers.
Where this film really becomes superb, IMHO, is in 120. Now if I get around to shelling out the money for that 80mm 1.9 for my Mamiya...
If I was getting the result I wanted, I don't think I would change it the night before the shoot just because someone said something.... even if that someone was an expert. I might take a backup camera with the new setting and might shoot concurrently, however.
If it is an indoor portrait, you aren't likely to encounter extreme brightness range anyway.
Based on my personal experience, I got a good result shooting Delta 3200 at ISO 1600 and develop it as if EI 2400 but that's with my camera, my developer, and my thermometer....
Seriously, I won't fool would what works this late in game.
DDX for 18 mins using 1+4 @ 20deg C shot at 1600 will work well and give finer grain than Microphen. But if its pure speed you want then Microphen is the developer of choice IMO. It really comes down to making a choice between speed or grain or what the lighting level dictates and if the lighting level really dictates a required speed of 3200 or 6400 then microphen is the best choice for a normal contrast negative. T-Max or XTol will give finer grain but you won't achieve 3200 speed with them. i.e. with most other developers you will lose shadow detail unless you expose at slower speeds which isn't what the OP asked for.
I hear time and time again people quoting ilfords ISO 1000 figure for D3200. But people just don't seem to know or understand that that figure is derived from using ID11 and not a push developer. Its called D3200 because thats what you get with microphen and not with ID11. And beating Ilford for promoting its own developers is a pointless exercise. Not only do they promote them but they develop and test films using their own materials. Infact they optimise their films and developers to work together. Kind of makes sense to use them together, especially if you want maximum speed film.
From all I've ever heard of this film - shooting at a lower speed gives you extra shadow detail (not a bad thing, given that you want a softer look for this particular shoot) while still getting that lovely grain.
FWIW, I've always shot this film at EI-1600 and developed for 3200. It's a unique film and another hit from Ilford, I say.