I have read that in order to boot Linux with the 32-bit UEFI, you can swap out the standard 64-bit UEFI GRUB with the 32-bit one from a different distribution and it'll be able to work on the Stream 7, so maybe a similar procedure (swapping the 64-bit UEFI bootmgr with the 32-bit one and reconfiguring the entries to match your installation) might work to get a 64-bit Windows installation running after you installed it with an AIO image with a 32-bit Windows PE.
However, after considering doing this myself on my HP Stream 7 that is currently on its way, I remembered the fact that the minimum requirement for Windows 8.1 x64 for memory is 2 GB, and the HP Stream 7 only has 1 GB. The installation size of a 64-bit Windows is also bigger (as it needs both 32-bit and 64-bit libraries for compatibility), which makes a difference since it only has 32 GB of internal memory. Those have to be the reason why HP even put 32-bit firmware on that device.
Windows Store apps won't care about running in 32 or 64-bit, and the rare desktop programs that would be 64-bit only are probably that way because they require lots of RAM and processing power, which the HP Stream 7 won't be able to provide anyways. So there is no point in installing Windows 8.1 64-bit on it, it would only use up more space and make it very slow due to insufficient memory. Of course, if you want to install Windows 8.1 Pro instead of the Bing version to have encryption and whatnot, go right ahead, that's what I'll do at least anyways. Or maybe try Windows 10 Technical Preview 2 once I know the tablet is fully functional and won't need to be exchanged.
TL;DR Just stick with Windows 32-bit, the Stream 7 doesn't meet the minimum requirements for the 64-bit edition and no program that requires 64-bit would run well on that hardware anyways. Just count yourself lucky you didn't buy a Windows RT tablet :)