You might find my own effort in this area appropriate to you: https://prooftoys.org/. Whether it is _exceedingly gentle_ is a legitimate question, but the site works hard to present logic and an embedded deductive system for learners whose background may be just ordinary high school mathematics. You might think of the website in these parts:

1) An introduction to logic through pictures, basically Venn diagrams with explanation. This is a point of view on propositional calculus.

2) A brief presentation of the rules of the logic of "simple type theory" at a raw beginner's level.

3) A number of completely rigorous simple proofs, some in pure logic, and some about real numbers, starting from the classic "complete ordered field" axioms that define the behavior of real numbers. The proofs are all done by computer from the ground up using the logic and axioms (with a handful of gaps). The proofs are all available for reading online, down to any level of detail, interactively, and at the reader's discretion.

4) A web-based tool that lets you build and edit your own proofs.

User feedback on the site is very welcome, and I will answer questions also as far as I am able.