I will contact Epson, and depending on their answer, I may try to talk the print service into using 360 PPI in the setting.
what is unclear is how the "print service" is submitting files to the printer itself. Depending on what they are doing they may not be using a "360" or 720 dpi setting. In a typical Photoshop setup, the file is sent without resizing to the printer, but with a specific physical dimension such as 8x10. Photoshop will not force an 8x10 image to a 2880x3600 pixel image, it will send the image at whatever the native file size is. The assumption is somewhere in the pipeline the image will get resized, presumably by the OS as an instruction from the driver, but I've even seen some debate about that. Unfortunately, however the image is getting resized, it is probably not using an optimal algorithm ... probably something simple such as Nearest Neighbor.
In this case, to make sure the service is sending the file at 360 dpi, you must resize it yourself to the specific DPI you are after, 360 or 720.
If they are a larger service, they are probably using a RIP, so it depends on which one they are using. But if so and the RIP is resizing before submitting, having the RIP resize to 360 should be their standard workflow. Check with them. But to make sure you can still resize the image yourself to 360 dpi. This gives you control of the process as well as the opportunity to apply final output sharpening at the correct output size.
If you want the image printed at 720 dpi, again it depends on many factors. First to gain any real advantage from 720 dpi, it's been proven you must using 2880x1440 and have the Finest Detail setting enabled. How specific RIPs handle this is a different story, because they bypass the Epson driver and manage all of this internally. But one thing is pretty clear, unless the native file size of your file at a specific output size ends up greater than 360 dpi, using the 720 dpi setting won't really gain any visual improvement.
One other note regarding the 1440x720 setting, there are actually two flavors of this setting. The printer uses horizontal passes, moving the paper incrementally for each pass to control the resolution. It has 360 nozzles covering one inch, so it can only print at 360 vertical dpi with one pass across the paper. This means to print at 1440 x720 dpi, it must make 4 passes per inch and at 2880 dpi it must make 8 passes per inch.
But some quality improvement can be seen if using 1440x720 dpi, and enabling the "Super Microweave" option in the driver. This means the printer will weave the data into 6 passes instead of 4, still at the same resolution with finer control. The results are pretty subtle. This option is not available for 2880 dpi because the printer is already making the maximum 8 passes per inch.
Most service houses use 1440x720 because the visual difference really isn't discernible, and obviously the output speed is increased (almost twice as fast). Additionally, many papers such as matt papers really can't hold the detail of the small dots well enough to make a difference. But if your files have enough resolution and you are printing on a high quality non-matt media, most will allow you to request the use of a higher quality setting