TVS diodes are designed to handle brief surges (hence the Transient in the name), so while they boast high peak power ratings, the acceptable continuous power dissipation is going to be much much lower (and you might not even see a rating for it in the datasheet). This is related to the fact that they tend to come in packages with fairly poor junction to ambient thermal resistance. A better bet is probably to use a second DPAK LDO in series to spread out the power dissipation. You could also use split the load into two separate +24VDC rails with their own LDOs, which would accomplish the same thing, but it may not be realistic depending on your load characteristics.
Alternatively, how close to 24VDC do you actually need your relay supply to be? Relays tend to tolerate a fairly wide range of coil voltages, so even if you can't go unregulated, you may be able to bump up the rail to 28V or something--obviously the coil current will increase according to its DC resistance, but this should still result in a net reduction in LDO dissipation (coil current goes up by 17%, but LDO series voltage drops by 40%). You could also implement peak-and-hold driving by simply PWMing the coil after it pulls in to reduce the steady state current consumption, but that's probably not necessary if the coil is only pulling 15mA.