If you think a plan would help you, make yourself a plan, but it has to be based on your actual life and opportunities, and ultimately add up to riding more, as everyone says!
Remembering to keep pushing myself rather than just pootling is the basis of what I do, though I'm not that bothered about speed I want to climb better, and I need to push my heart rate for that.
Intervals of some sort on the rides you already do is the obvious way to start. I don't use strava, but I do have a heart rate monitor and a cadence thing on my road bike, so I try to increase my cadence when my heart rate is at a good working rate (145 for me) so whatever cadence I'm doing I aim to round it up for the next few minutes of my ride.
I also train at the gym with a PT for ten weeks before my summer hols cos I want to do Alpine climbs, and I need focus for that. This is my third year of forking out for this, and it really helps me... The gist of what he does with me is increase the time I can work at a max heart rate (155 for me ... it is what i can sustain and climb at) in a high gear. We use a spin bike for that, increasing the resistance and time intervals each week to build my endurance, which I guess you need for speed as well as climbing. I also do single minutes in a medium gear @ very high cadence with minimal recovery time.
If you are a gym member, use a spin bikes on your own, not the static gym bikes, or do a spin class and work harder than the instructor tells you to! You can really see your progress with this.
We also do work on core stability, which helps keep your upper body stiller under pressure, useful for balance when climbing, and maybe to energy conservation at speed? My PT uses gym gadgets that make me wobble, but if you aren't a gym member you can do similar at home by doing planks on your elbows and pushing up to your hands, and back to your elbows again, without losing the stability of your plank posture. Over and over till you collapse. Also, from a plank on your hands, bring your knee in to your elbow on alternate sides, without losing your plank stability. I think they call that mountain climber. If you can't visualise what I mean, then a bit of looking in YouTube for core stability should find demos of the exercises which help.
I also totally agree with whoever suggested using my fitness pal app. It is brilliant. You have to get used to portion control, and weighing things so you really know what you are eating, but once you know what 10g of butter looks like you'll be much more aware of the calorie density of fats...
Otherwise, Aim to eat as much healthy stuff as you can and still lose weight!
I am in a constant battle with me weight, but all these things help. Good luck
This is me, up Galibier last year. It was slow, but I hauled this 12 and a half stones up there!