I agree that you should be using your own miles. I'm 6'5" and I had the same problem. There was no way I was going to fly coach that far squeezed into a tiny seat with no legroom.
There was another person at my company who stamped his foot down and said he wasn't going anywhere if they didn't pay for J.
We gave him his J ticket and never sent him back for another trip. I figured out how I could make the situation work and never dreamed of asking them to pay for something as silly as a paid business class ticket (these things are outrageously expensive and I don't see how anyone justifies their expense). I used my carrier, UA, even though the routing to India was awkward at first (ORD-SFO-NRT-SIN-BLR vs. ORD-FRA-BLR on LH) ebcause I could earn and spend my miles. I work hard everytime I need to go to find the flights that work and put in a minimum of 3 hours on booking my tickets to make sure I get what I need without making silly demands. I also now book tickets for a couple of other people when they need to go (including our CFO who used her own personal miles to buy an award ticket in J).
In exchange, I go whenever I want or need to, I get to see the world, and my employer finances my 1K status. At first, I didn't have SWUs, so my mileage balance didn't grow (I'd earn 40,000 miles for a trip to India and 20,000 domestically in the months in-between and spend 60,000 miles on a round-trip upgrade), but it wasn't hurting me. Now that I've flown enough to be a 1K and get SWUs, I use those for both my travel and even gave 2 to a coworker so he could upgrade.
Sorry. I'm just not sympathetic to the idea that you don't think it's important enough to spend your own miles on.