Calculating resistor values for N3904 transistor
For R_I I want to: limit current to the 555,

R_I is connected to pin 2 which is the TRIG input which is a &quot;high impedance&quot; input meaning that it draws (almost) no current. 680 ohms is a bit low, I'd use 10 kohm so the current stays low (below 1 mA) and there is no need to have more current flowing there

limit current when the transistor is on,

Indeed you should not make R_I too low as then too much current can flow through the NPN transistor. But if you do make R_I too low then it will heat up way before the 2N3904 hits the highest current it can handle. Realize that when the NPN is on, there's about 12 V across R_I.

not drop too much voltage which would cause the 555 to be triggered.

That is no issue, because there will be (almost) no current flowing into the TRIG input.
The current is actually so small you can safely ignore it.
R_S is 10 kohm and that's perfectly fine.
So only increase R_I to 10 kohm as well and you're good to go.