Looks good so far. Just don't remove the lower branches, you want to take weight out of the top of the stem.
My suggestions from what I can see:
- lower branch heading to right - thin tips by 20%.
- main branch junction straight up from the fireplace 1/3 from top - subordinate the tallest branch and thin the rest
You don't want to lion tale (strip all the small branches except for a tuft at the end). Growth hormones focus on areas around the leaves, so if you lions tale a branch, it grows in diameter only near the leaves giving you a long skinny branch which is more susceptible to breakage. If there is foliage along the length of the branch, you will end up with a branch that has more taper and is stronger.
A clear example of this concept is comparing an open growing conifer with branching to to the ground, usually has a large taper to it, whereas a tree growing in a dense forest only has foliage in the top 10% of the tree but has a long straight stem with little taper.
As I mentioned before, in about 5 years, I would reduce this stem further. Ultimately (after several 5 year pruning cycles), due to the foliage reduction (loss of growing capacity) the stem will reduce in size IN RELATION to the main stem. Once the stem becomes 1/4-1/3 the diameter of the mainstem, it could be removed.
In you case, you probably won't be alive/live in that house that long, so I think reducing it will be sufficient.
Where the branch initiates in the tree, there is differentiation between the branch wood and the trunk wood. There is a certain amount of compartmentalization around the branch wood or else any dead rotten branch would lead to trunk decay, which it obviously doesn't.