I have two suggestions...
Option #1: Separate ESPs
Under EFI, the boot loader resides on "the" EFI System Partition (ESP). I put the word "the" in quotation marks because there's no rule that says you're limited to one ESP. If you create two ESPs on your hard disk, you can use one of them for your first installation and the second ESP for the second installation. This should work pretty seamlessly, although you'll have to create your partitions manually (using the "Something Else" option during installation), at least for your second Ubuntu installation.
One problem with this approach is that, although the EFI specification explicitly states that you can create as many ESPs as you like, some software might become confused by it. One prominent example of this is the Windows installer, at least through Windows 7 (I don't know about Windows 8 or later); when the Windows 7 installer sees a disk with two ESP, it flakes out and does weird things. IIRC, it doesn't complete its own installation properly. It's conceivable that Windows repair tools would suffer from the same problem. If you're not booting Windows on this system, this shouldn't be a big deal. If you are booting with Windows, you should simply be aware of the problem, because you can easily overcome it by temporarily changing the type code of the non-Windows ESP(s) if you run into problems. Note that Windows will boot just fine on a disk with multiple ESPs; it's just the installer that chokes on such disks.
Another issue is how you'd switch between your two distributions. You might need to customize one or both of your installations' GRUB setups using a tool like GRUB Customizer. Another (but not incompatible) option would be to use your firmware's own boot manager to switch between your two GRUB installations, and use each one to boot just its own version of Ubuntu.
Option #2: Abandon GRUB (or at least Ubuntu's GRUB tools)
The problem with GRUB for your situation is that you've got two installations and the GRUB maintenance tools are likely to become confused by that configuration. This observation leads to the obvious solution that you should simply not use those tools. There are several other EFI boot loaders for Linux, most of which are easier to manually maintain than GRUB. You could set up ELILO, SYSLINUX, Fedora's patched GRUB Legacy, gummiboot, or rEFInd and manage both your installations manually. In fact, because rEFInd detects kernels whenever it boots, rEFInd should be close to no-maintenance, once it's set up. Alternatively, but in a similar vein, you could hand-edit your
grub.cfg file to do what you want, rather than rely on the GRUB setup scripts.
Aside from rEFInd, all of these tools will require you to make configuration changes whenever you update a kernel, which will be a drag. There's also the question of when and how to install the extra boot program. I'd probably put it off until after your second Ubuntu installation, since each installation will register its own copy of GRUB as the default boot loader, and you want to override that default.
Note also that none of these tools can read a kernel from an encrypted filesystem or from an LVM, so you'll need to have a separate unencrypted
/boot partition for each of your Ubuntu installations. This is the way most instructions I've seen say to set up an encrypted Ubuntu installation anyhow, so it's probably not a big deal unless you want to play on the "bleeding edge" of disk encryption.
Some EFI boot loaders have additional specific partitioning or filesystem requirements. Most notably, ELILO, SYSLINUX, and gummiboot all require the kernel to reside on a FAT partition, and the ESP works best for this. You can do this by mounting the ESP at
/boot, but this is an iffy solution in Ubuntu because some package updates require symbolic links. You'd also have trouble doing this with two separate Ubuntu installations because they'd both try to claim the same files. (In this case, "the ESP" really means "the partition from which the boot loader ran," so you can have just one ESP in this case.) GRUB Legacy and rEFInd are more flexible about this.
Personally, I'd use rEFInd for this -- but as I maintain rEFInd, I'm not exactly unbiased. In fact, I've got a computer that multi-boots between three Ubuntu installations, and rEFInd switches between them just fine. This particular system doesn't use encryption, but I doubt if that will cause any new problems from rEFInd's perspective.
That said, separate ESPs should work fine, too, with the caveat that you might need to use GRUB Customizer to tweak the settings of at least one of those GRUB copies.