I have not used suction cupping, but if you are seeing improvements with it continue doing it.
Have a plan 30 minutes of mobility work 2 or 3 times a day. Morning, night, and if you have the opportunity to spend time during your lunch at work that may be another option to work on it.
Doing strength 3 times a week works.
If adding weight to the bar work continue doing it.
If aren’t able to add weight to the bar for something you may consider getting a heavier bar. Sometimes you can find used bars on Craig’s list. You may not be ready for a heavier bar.
You can get everything from Rogue Fitness:
Voodoo Bands 
Jump Stretch Band  1 option OR 2nd option
Supernova
Gemini 
Therabands don’t have enough resistance. You will not have a problem with jump stretch bands or their durability. You want a green and a blue.
Yes you can use them for x band walks. This video shows someone using one How to do xwalks
Yes doing a dynamic warm up before mobility work could help. Message me if you want ideas on it.
Warm up and mobility work are 2 different things so yes a warm up is helpful.
When I workout I wear shoes. You want a flat shoe DC, Vans are a good option, Nanos, All-Stars. For Oly sessions wear Oly shoes.
For every day life something flat DCs, Vans, All Stars if you need a dress shoe there are flat options there.
Orthotics may be worn for some time, but you want to strengthen your foot so your foot is making the change not the orthotic making the change for your foot.
Have you watched the Rebuilding your feet 3 videos or the Flat Foot Solution?
Start here for moving away from wearing orthotics.
Yes you should go barefoot at home whenever possible.
If you wear a wedge in your shoe you should always wear it.
Going back and fourth can throw things off and cause you to make compensations when you don’t have the wedge in your shoe.
I asked before, but is this something that can be corrected having a chiropractor adjust your hips/pelvis?
I ask because I know someone who had a situation like this rectified. At first it can take 3 adjustments per week moving to 2 then one then when needed as the muscles learn the new positioning and can hold the position.