HR isn't much value to anaerobic intervals as it's too slow to respond. I would find a short hill that takes 30 to 90 seconds to climb and do 5 to 10 repeats with 3 to 5 min rest between intervals. Goal is to ride them close to all-out at a steady pace, i.e. as hard as you can go while maintaining steady power. I'd use the geared bike as you'll likely end up putting out lower power with the fixed gear due to sub-optimal gearing.
I've got a local hill with 50-60m of elevation and 10-15% slope that is perfect for these intervals. My arms end up quivering at the end of a session. They're kind of painful but on the bright side your workout won't take long

Here's a typical workout for me. I have power but don't really look at it when doing the hills. I mix up the gearing a little and do some sitting and some standing: