I'm not sure if Celerity is too strong. It's the generalist option and it has good synergy with Waterwalking. It's the go-to rune because everyone wants MS unless there is some other specific synergy and it comes online immediately. A rune like Transcendence is only situationally useful and isn't something you want to take as much if not in a solo lane. Basically, It's easy to think that because lots of people take it, it's actually OP. I don't think it's that simple. The others are quite niche and it's thus expected that Celerity would dominate (especially in fast metas).
Now, let's look at the proposed changes:
Movement speed lowered from 3% to 1.5%
Adaptive AD increased from 4.8% to 9.6%
Adaptive AP increased from 8% to 16%
These are potential buffs for champions with built in MS bonuses such as Singed, Nocturne, Hecarim, and Trundle but a nerf to the rest. Essentially, it takes Celerity and makes it more niche but in a somewhat artificial way. It becomes more tied to kit rather than playstyle. This is the opposite of the stated goals for the rune system. Perhaps it should not offer any AD or AP based on MS at all. This will always provide far larger advantages to some champions over others.
Right now, at least it is primarily about playstyle rather than champion kit (even if it may be the most successful playstyle). This change risks making champion balance dependent on Celerity and may turn it into a non-choice. It may become a binary decision based on whether you have special synergy and if that synergy is very strong, it'll also definite the meta. Most problematic, on those champions with synergy, there will be no option because everything else will be far worse by comparison. It's likely that some champions will even get nerfed as a result of it and thus will become even more tied to Celerity for viability.
Thus, while this may be a decent rework option, there are also dangers which need to be carefully considered.