The relay should be fine. You've got the contact part of the relay correct.
The coil, with its series resistor, should be wired to where the 300 V lamp was connected. In other words, the one side of the relay coil should go to one connection that used to feed the 300 V lamp. One side of the resistor should go to the other connection that used to feed the 300 V lamp, and the other sides of the relay coil and the resistor should be connected to each other and nothing else. (You have shown that)
We don't know, and there is no need to find out, if the 300 V circuit is connected to the 120 V supply. Therefore you should not have any common connections between the contact side of the relay and the coil side of the relay. Your circuit has the contact "A" wired to one side of the coil, which may be wrong. It is safest and easiest to keep the two sides separate.
With that relay, you need a 15 kΩ resistor, rated at 3 W or more. You need to buy a resistor that is rated for 300 V ac. It will have to dissipate between 1 and 2 W. Power resistors run really hot at their full rating, so a larger power rating keeps things cooler. I suggest something like
https://www.digikey.com/product-detail/en/UAL10-15KF8/696-1424-ND/3886628
I know that is very generously rated, and if this were a commercial product it could be worth saving a couple of dollars. However, the full 12.5 W rating for that resistor is with a big heatsink and with a case temperature of around 250 °C, in an ambient temperature of 25 °C. If you don't have heatsink, and it dissipates 2 W, it will still probably be too hot to touch.
That is the cheapest panel-mount 15 kΩ resistor that Digikey offer.
The relay voltage that you will get with 15 kΩ is likely to be between 180 and 250 V, and the power in the resistor between 1 and 2 W. The uncertainty is because the relay data sheet doesn't quote the coil inductance and resistance separately. The inductance and resistance combine to create the impedance. The impedance can be calculated from the fact that the relay takes 10.8 mA at 240 V, but the effect of adding a series resistance is not known exactly without knowing the inductance or resistance. It would be a very good idea to check the voltage across the coil when you have connected up. It should be in the range 180 - 250 V, which should be within the acceptable range for the relay, but if it isn't, tell us the voltage (and measure the 300 V supply under the same conditions) and a more accurate resistor value can be worked out.