If you are a naturally patient person please ignore this post.
I TOTALLY understand your patience comment. I have a high rpm motor in my head and I sometimes imagine I should know things that there is no way I could actually know. (Ask my wife sometime.)
Something I learned about patience working on my engine. I cannot be patient if I am not doing whatever I can to make myself comfortable when doing slow patient work in my engine space and make it a rewarding(for me) process.
For me this means: 1) Knee pads. My Husky knee pads help me focused on my engine work and not my knee pains when I am jammed or balancing for long periods of time. 2) Padding on the engine when doing cold engine work. I remove ignition cables and lay a couple of foam pads on top of my engine, it seems like in the Pearson 30 I am forever spooning the entire engine head to get beside and behind the engine. (Engine work actually reminds me a lot of bouldering/rock climbing)
3) Preparation. (I don't want to short change my learning experience) I probably spend 4x the amount of time researching, planning, sketching, and studying systemic cause/effect, chain of function, etc before I dive in. (Even then I make some whammo mistakes!) 4) Documentation. This helps me manage the risk of missteps and it gives me immediate/future feedback and reward for all the small steps required by much of this new-to-me engine work.
Regarding fuel system. The best advice I got and give is to segment the system upstream first.
Test and evaluate your tank (what degree of cleaning needed?), here is the rig I used (inspired by others here). To inspect gasoline condition and sample tank for sludge.
https://photos.app.goo.gl/wbid8CM15DotBK8d6 long pvc pipe reaches bottom of tank.
If I had found even a little sludge I would have added agitation to detergent treatment. Tested then considered service in place or removal to clean. I have Monel tank. Any detergent of solvent or agitation approach needs to be matched with tank material.
https://photos.app.goo.gl/4LDiwrYDzqnMSuX37
https://photos.app.goo.gl/7BfhJkReqaeixDNy8
https://photos.app.goo.gl/WTRCb5o876at97vV6
I was very fortunate in that all upstream evidence indicated acceptable tank, tank fill, tank vent, and tank cradle conditions.
I have a little weasel in my head that sometimes wants to short-cut diagnostics. To counter the weasel I ask myself repeatedly if I have collected enough information and especially looked for confounding data that I would rather not seek.
Then it was time to trace fuel hoses check valves and clamps. Check fuel filter. My PO had replaced all hoses in past 7 years. So no ethanol decay worries.
Then is was time to address pump, pressure, carb.
The "mind weasel" tested me at every turn. One thing about this forum. It is a "mind weasel" slayer. Choosing to ignore experienced rigorous(mostly) thought-out posts makes one face the timeless question "Am I solving the problem or eliminating the symptom?"
Best with your journey and destination. Stay well.