Nick, Lyme disease, Babesiosis and Bartonella did damage to my joints.....as a result some of the issues are tough to overcome and I am a fighter. So, when I say it is tough to overcome, it is tough. I have about 6 months to a year of Bartonella treatment and hopefully will feel much better at that time. I also, as a result have something called MGUS (I won't go into details) and this also can cause peripheral nerve damage and muscle, tendon, ligament issues. So, the that is a big problem for me.
Soreness? Well, if I work out hard....I am sore for 2-4 days. The DOMS hit about 48 hours later and then I remain sore for another few days. Why is that weird? So, you see...there is no way I am doing squats on Monday and squats on Wednesday. I'd be doing but copnstantly breaking down muscle with little room to rebuild. Maybe if I took steroids.
If I follow my routine, lets say I end up hitting some of the same muscles three times...indirectly. Your listed program hits the muscles three times in one week. In light of that, I don't see an issue with my routine. We may both experience great results. But I don't think I will really make large gains till I am through this damn illness.
I am not even a fan of doing squats and deadlifts on the same day because after a brutal set of squats, I feel deadlifts can be redundant...especially with a trap bar.
Mon: squats, deadlifts
Wed: bench, dips, press
Fri: pull ups, barbell or dumbell rows.
I sympathize with your situation, but might I suggest working through the soreness? From my experience, it helps, and if you let the soreness dictate when you do your squats, or your deadlifts, or whatever - those exercises are always going to leave you sore, because you're not letting yourself get used to it. It's like putting your toe in a pool, then waiting 20 minutes and doing it again to miraculously find that it's still cold. Only after you jump in and swim around for a minute or two does it get comfortable. Of course with lifting, we're dealing with different rates of adaptation, and the adaptation remains with us for longer than 20 minutes, but I'm sure you get the point.
Of course, there's a difference between soreness and serious pain, which would suggest injury. For example, joint pain is never good.