Whole disk encryption on a tablet (that has no pre-boot keyboard)

Question

I am researching methods to encrypt whole disk on tablet. I would like to encrypt my tablet that comes with Dual Boot OS, with pre-installed Windows 10 Home and Android 5.1.

Let's start with what software can be used to encrypt whole disk:

1. TrueCrypt 7.1a
2. BitLocker
3. Something else ???

TrueCrypt:

On laptops I simply use TrueCrypt 7.1a, I trust this method and i'm not on the "TrueCrypt is dead" crap. But on tablet I am facing two problems:

1. My tablet comes with hard disk with UEFI GPT (GUID Partition Table). And TrueCrypt support only drives with an MBR partion.
2. My tablet has no pre-boot keyboard, so you cannot enter the pre-boot authentication password.

Solution for first problem is to convert disk partitions to MBR and use legacy BIOS compatibility. But in the process of this whole disk will be wiped, and I will lose my pre-installed Windows 10 Home and Android 5.1. So next I will need to reinstall OS. I think, I do not care about Android. Question is, if it will be possible to reinstall Windows - I never installed Windows on tablet, it has no DVD Drive, but I think I can use USB OTG cable. I suppose Windows installer is adapted for use on tablets.

Solution for second problem, is to use external physical keyboard. I suppose bluetooth keyboard will not work at level of boot menu. So I need USB external keyboard on OTG cable. But there goes the portability function of a tablet, we lose the aspect of mobility. So we need to use something very very small that will act as a USB keyboard. We can use YubiKey device programmed to emit static password.

It looks that it is possible to use TrueCrypt on tablets.

BitLocker:

With BitLocker things are simpler, it support GUID Partition Table, so no need to reinstall system. And I have read that it also have some simple on-screen keyboard to enter the pre-boot password. Problem is I have pre-installed Windows 10 Home and BitLocker support is only with Windows 10 Pro. So I need to buy Windows 10 Pro Pack 99 USD. So one minus is I need to pay. Second, I don't trust BitLocker, Microsoft is widely confirmed to co-operate with the NSA, they are putting a backdoors into their products(skype confirmed), and since BitLocker it's closed source who knows what's inside.

Something else:

At Wikipedia is article with comparison of disk encryption software, and there are another thirty software that support whole disk encryption. Do you know any of them support tablets (prefer free solutions)?

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Best option for me will be TrueCrypt, but I'm a little afraid to try, I do not want to break my tablet. So I really wonder should I give a try to BitLocker?

My tablet (if it's matter), is Teclast X98 Pro Dual OS Windows10 & Android5.1.

I ask here for any advice. Someone with any experience with tablet encryption?