Carl_This was a motivating read! It sounds like you have a fantastic foundation routine, that's awesome! I pulled up the videos so I could see what you mentioned, everything looks generally solid. My focus was track which has tons of rehab / form focused activities associated to it.
Your schedule is reasonable, adding the extra 3x10 sessions is good for variation and gradually pushing outside comfort zones. The breathing issue will resolve and is expected with cardio. Sustained / consistent pace will help that. If you notice you're gassed to the point of needing a break during a set, try slowing the pace next session so you can meet your full set time. Needing to stop will happen periodically but you want to "force" sustained activity that is comfortable while moderately challenging yourself. If I notice that happening on runs, tip is deep breath while pulling shoulders to ears then drop shoulders (pushing down through shoulder blades) on full exhale and lift knees / pump arms / slow pace. It helps relax the natural tension that builds while running and tricks the body into re-syncing optimal rhythm. Awkward at first but when applied becomes muscle memory the moment tension is noticed. Shallow breathing or gasping is usually shoulder tension restricting the chest / lungs. Slowing pace is better than dead stop. Rather than going right into session, try a 3min warm up - nice and easy. From what I saw on video, I would say high knees with gentle side lunge / back step. Nothing intense, more focused on form. This should also help reduce activity tension leading to feeling gassed.
Playing with your session times is also a hack that is easy to do. It will prevent your body from finding a set rhythm it expects during activity, ultimately becoming too comfortable.
For 25-off-10, adjust your rest time. One day rest for full recovery, one day rest for 3min, one day only 1min (listen to your body and pace within your comfort level). You will have to set sustained pacing to hit your times without needing to rest before you hit your rest set. This will help deal with conditioning lungs. Add those extra 10s periodically with varied rest times as well. Initially pair full recovery sets together. But eventually if you take a full recovery on first rest set, second rest should be the shorter of your decided recovery times. I would run this style of conditioning 4-6 weeks.
Then I would consider going 20-off-20 while dropping the extra 10min in this phase initially. After a couple weeks add that back in. You should be noticing increased energy here. I would start with full recovery between all sets, then adjust as you notice second set becomes easier. Add your extra 10s again but increase them to 4 times a week. At this point add a second rest day. But where one day is full rest, your second rest day (mid week preferred) is active recovery - a single set of 15-20min at reduced pace. You want your body be active but reduce load since you will be straining muscle and joints. This helps with injury prevention as you ultimately are increasing overall exertion by this point.
I imagine if you're already doing 6 sessions a week, it will be no time before you're comfortably hitting 5 days of 20-20-20 and 20-30-20 with ease at increased pacing.
Following a similar outline for conditioning, last summer I was running 10k around 48min wanting to drop to 41 while not being a trained distance runner. Currently I'm doing weighted jump rope until the snow disappears - 4min, ladders 2-3-2, 3-3-3, and varied time up to 35min using a playlist for on-rest. But I can only handle 3-4 sessions a week.
Just general suggestions, apply what you feel is relevant or adjust ideas as you need. Listening to your body is key but pushing reasonably outside that comfort zone for variation is key.