If you want to build a PC archetype (and actually play it), but the rules do not service the archtype well, ask the DM to allow some modifications. Some DMs will turn you down. Others are going to put player fun above absolute adherence to the fine details of a rule, and will allow you to make some modifications. As a note - some DMs are insanely against thee types of modifications and can be quite rude when they are discussed.
If a player wanted to play a Tortle Monk in my games, and said they were discouraged that so much of the Tortle abilities were lost on a monk, I would offer the following adjustments:
* You can use your claws as Monk Weapons. [Net effect - they get the option to deal slashing damage with their monk unarmed attacks].
* If you have not moved since the start of your turn, your AC from unarmored defense increases by one. [Net effect - you get a little defensive bonus for holding your ground and using your shell, but only when you don't move].
Neither is game breaking, and they both allow the 'Tortleness' to shine through. Of course, someone will likely respond that a suggestion like this is going to murder kittens, so YMMV.