I'm close to the numbers you want to reach and I began the basic 5/3/1 template 6 months ago.
Started out that I was 176lbs, somehow dropped to 170lbs in the first few months and now I'm back at 176lbs with some body recomp (that wasn't planned at all but not gonna complain about it).
If you're 6'2'', I'd look to put on a couple pounds first without stressing too much about "aesthetics". Commit to gain some weight AND focus on getting stronger, your aesthetic will improve too even if you gain a few points of %bf.
With that said, there's too much stuff in your layout. Leg curls, leg extensions, different cable flys, you'll just wear yourself down with all that stuff - and it will be useless.
Be much more conservative at the start.
Do PR sets or 5's Pro as your main work, then follow 5x5 FSL with the same lift (using the % of the first main work set), then pick just a few sure-bet exercises for assistance - rows, chins, dips/pushups, leg raises, lunges depending on what main lift you're doing.
Get used to superset the assistance work with the supplemental (or even main) work, i.e. doing leg raises between sets of deads or rows between sets of bench.
The goal is to do the best you can with maximum effort on the main work, focus on bar speed and technique on the supplemental work and increase work capacity with assistance work - you don't want to kill yourself with assistance stuff, you don't want to reach muscular failure and you don't even want to end your workout completely drained. That's not the point of strength training but you can bet you WILL pack on mass/size anyway.
Do the basics for a few months, get a grasp on how the TM works, how you need to focus on bar speed and technique, then you can move to a more specific template - for your goal, Boring But Big sounds good (but you have to be honest with your TM and bar speed, it's not a template you can grind away). Like, 3 cycles of BBB, then follow up with either the BBB Challenge or the Beach Body Challenge, a few people here did them and can probably give you more feedback.
So take into account that if you want to reach a certain strength level, you have to focus on that for some time. Once your strength is up to par, you can push more towards aesthetics by reducing the strength work and increasing the bodybuilding work.