the primary things that will get you climbing faster are

1. raising power (ride the bike more)
2. losing weight

Climbing specific work will be a bit of icing on the cake but you are already climbing pretty often it sounds like.

Have you talked to your doctor about different treatments for your asthma so that it doesn't interfere with your workouts? That could also be a huge limiter.

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Kat Hunter reports on the San Dimas Stage Race from inside the GC winning team
Aeroweenie.com -Compendium of Aero Data and Knowledge
Freelance sports & outdoors writer Kathryn Hunter

Your cadence seems high enough and you're at/below threshold, so you're doing effective training and don't seem to need an easier gear.
Agree with Jack that weight and possibly the asthma are your biggest limiters.

Keep doing what you're doing. 45 minutes at sweet spot is a good session.

I agree with Jack. You literally have to climb zero mountains to improve your climbing performance. Most of your climbing training can be done on a trainer with a weight scale before every ride...get the watts up and weight down. Then show up with the right gearing so you can hit the target climb in the right weight range. I'll give you an example. Last month I climbed a hill call Sierra Rd outside San Jose CA in 30.40. All my riding was on the trainer. Not a bad time, but room for improvement. Next month I showed up 1.5 kilos lighter (went down from 64.5 to 63 kilos). This time I got down to 29.09. Slightly better pacing tactics early in the climb, but most of the diff was just losing the weight. Unfortunately, I don't have an estimate of my watts, but I am pretty sure based on my computrainer rides, that they did not change in the last month by much.

Jack & Paul are correct. People over think hills. Hills are really easy as compared to wind. With wind, you have to consider wind direction, equipment selection, position on the bike as well as improving power output. Plus hills in North America usually only last 5-20 minutes or so. A headwind can last for hours on end. Plus hills don't change grade or change direction. They are what they are, all the time.

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TrainingBible Coaching
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Wish I could be at 64KG ;-) I think I weighed that when I was 13. If you see me, you would not think I have any weight issue, broad shoulders.

When I was running seriously in my mid to late 30s, without really watching my food intake, I weighed at my lowest, 160lbs, and that might have been after a run.

I struggle with getting the weight down, and I'm told that some of the asthma meds cause weight gain. I need to learn that go hungry to bed thing.
When the weather gets better, I sometimes climb Cypress before breakfast.

Met with my asthma Doc this week, and he said we need to get aggressive as it's obvious there are problems. (He's actually a former national level cyclist)

So, on special antibiotics for 3 weeks, increased meds, chest x-Ray done and CT Scan coming up.

Have a nice climbing event coming up May 3rd, 140K, 3000M of climbing

This photo is from this past February on Cypress, the mountain in the Strava file. No snow, the ski hill was closed.

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Cervelo R3 and Cannondale Synapse, Argon18 Electron Track Bike