If you can, start by moving your business expenses to a Mileage Plus business card. Your $100k could earn you over 200,000 miles, which in itself pays for more than one international first class round trip (or close to two business class round trips.)

Then, look into acquiring 1K status, as you'll earn 6 GPUs a year, which allow you to fly your 6 trips in business class if you buy economy, or first class if you buy business. In some cases, you may get double upgrades by paying a fee in addition to using a certificate, but it's a crapshoot.

Now, to set expectations.... whatever you do, it's going to take some effort and adjustments. As you put it yourself, "All I want is first class on 6 overnight flights a year" -- that is quite a lot to ask, if I may say, coming from someone who typically only makes Silver or Gold

If flying more is not an option, then there's always other tricks to earn miles (credit card churns etc.) but it's going to take a lot to fund that much free travel. (Oh, and after next year, forget 1K without a significant increase in spend.)