I suggest you use the zero-chamber reactor I linked to in my earlier post. 100 EU/t isn't 120, but quarries have diminishing returns on higher power input anyway so you'll hardly notice the difference between 40 and 48 MJ/t.
Next, set up an emerald transport pipe with an autarchic gate on the reactor. Set the filter in the emerald pipe to only pump out "near-depleted uranium cells". Those are sometimes leftover when an uranium cell expires. Set the autarchic gate as "space in inventory -> energy pulse". The pipe should ideally lead to a storage chest, of course.
Then place down another chest two blocks away from the reactor and fill it with uranium cells. Use a wooden transport pipe followed by a diamond transport pipe to connect the chest to the reactor, and branching off from the diamond pipe, build a loopback to the chest. In the diamond pipe interface, place an uranium cell in the exit leading toward the reactor. Place red pipe wire on both the wooden pipe and the diamond pipe. Place an iron OR gate on the diamond pipe, and set it to "space in inventory -> red pipe wire signal" and "no space in inventory -> redstone signal". Place an iron autarchic OR gate on the wooden pipe, and set it to "red pipe wire signal -> energy pulse".
Make sure you do not have a lever attached anywhere; the iron OR gate supplies the redstone signal to turn the reactor on so long as it is filled with cells.
This may sound convoluted, but it really isn't - and keep in mind that once established one time, you can re-use this setup with however many quarries you wish.
What happens is this: as soon as the reactor runs through its first 2:46 hour cycle, the uranium cells will disappear, and the "no space in inventory" condition on the diamond pipe's gate becomes false. This means it will stop outputting a redstone signal, which in turn means the reactor will turn off.
Also, the "space in inventory" condition on both attached gates becomes true, triggering the autarchic gates. The emerald pipe will remove any leftover depleted cells that may have spawned (you can throw those in a breeder later), while the wooden pipe supplies fresh uranium. The diamond pipe will force the first six uranium to go directly into the reactor, but as soon as that is full, the remaining cells in transit are allowed to try the alternate exit, which leads them back to the uranium storage chest (instead of spilling out, which would happen without a loopback path).
Finally, as soon as six new cells have been inserted, the "no space in inventory" condition on the diamond pipe's gate becomes true again, reactivating the redstone signal and thus turning the reactor back on. At the same time, both autarchic gates are turned off.
Thus you have a fully automatic reactor that will keep running as long as it finds uranium cells in its supply chest to keep replacing the consumed ones. You could plop down a big chest with lots of uranium cells, or use an ender chest and have an autocrafting system in your base continually provide new cells (just make sure you always leave some space for the cells returning via the loopback). The downtime between cycles when swapping in new cells should be in the neighbourhood of 10-15 seconds, so the quarry will not even finish slowing down before the reactor goes back online.
Have fun!