I'd go further than that and scrap the entire county championship. Replace it a regional comp of six-eight teams.
The counties might complain but what are they going to do? The majority are loss-making entities and depend on the ECB for support.
As for the structure, go back to the old Sunday League system and alternate between T20 and four-day. Keep the Hundred block as it's clearly financially viable and gives players a chance to practice white ball skills exclusively.
Finally, introduce more 'probable v possible' - type matches and have more A team fixtures. England Lions should be playing all the time, even more than the full England team.
I see no harm in the county championship continuing at the level below to some extent (and also don't see how it could be prevented, unless the counties were fully amalgamated into the new franchises, they cant force counties to close and running their own comp). Whether the county championship would then lose first class status I don't know, or maybe be adjusted to 3 day games like minor counties. I expect either way the clubs would struggle financially, but they also own prime real estate in the test venues, and would be required to develop players to progress to the franchise system, so there would likely need to be some level of amalgamation with the regional franchises. A few of the smaller counties might have to become non professional.
Personally I see a top tier of the franchises playing all formats, but smaller number of teams so condensed quality. A second professional, first class tier below of the strongest counties, and below that a third, semi-pro, non FC status tier containing some of the smaller counties who can't remain professional, and perhaps some spaces for the better minor counties sides. Franchises could either sign players for the whole season or just individual comps, allowing them to play at the level below if unpicked and it still be a high quality.
As for number of franchises, I do think 8 might be too many. I enjoyed the Hundred despite being sceptical at first, but I thought there were too many games and I started to lose a bit of interest towards the end, plus there were a few players involved that were not at the same level. I can't quite get 6 teams to work, so personally I'd consider doing just 4 franchises of super condenses quality: Northern and Manc combining as one Northern franchise (essentially Lancs, Yorkshire and Durham), the two current London franchises combining as one Greater London side (Surrey, Middlesex, Kent, Essex), the two current Midlands franchises as one (Notts, Leicestershire, Derbyshire, Warwickshire, Worcestershire, Northants) and then the Southern/Welsh franchises merging to form a South-Western team (Somerset, Gloucs, Glamorgan, Hampshire, Sussex). Super condensed quality, the best domestic players all competing to prove themselves for England selection.
With the format proposed, the aim should be for England players to play as many of the franchise games as possible given the international schedules, as there are few of them, and not be dropping back to the 2nd tier for games (unless it's as part of coming back from injury and building fitness). Say home and away in each comp, that's 6xred ball, 6x50 over and 6x100 ball games. Like you said, I'd do the format of red ball games during the week and then the 50 over comp at the weekend, with a block in the middle for the Hundred. In total, Franchise cricket would only take up less than than half of the playing calender, but it would be high, condensed quality. Franchise players who don't play for England would also compete the remainder of the season at the 2nd tier level, and likewise, the 2nd tier players who don't get a game once the franchise players are back could be loaned to sides in the 3rd tier for game time - essentially creating a trickle-down system of quality. It might also be worth the 2nd and 3rd tiers both competing together in the T20 comp, as its essentially the only comp at county level that has big attendances.
Note: after typing this all up I have realised a way to make it 5 or 6 franchises, but I cba to edit this long post, and the details would remain essentially the same whether 4, 5 or 6 franchise teams. There'd also be the option to have 8 franchise teams for white ball, but have the red ball as just 4 franchises. I'd also consider having a link between the franchises and counties, eg the London franchise could only sign players from the London counties. Not sure that fits with the auction format, but I found the auction pretty gimmicky anyway.