The benefit of a high dynamic range image is that you have a much larger intra-scene dynamic range than you do with SDR. The black level and average scene brightness should remain the same for both SDR & HDR, but the max luminance should be dramatically brighter with HDR imagery. If you're viewing an indoor movie scene with no specular highlights, for example, the scene brightness should be the identical for SDR & HDR.
Those HDR benefits are available if you're viewing a FALD LCD display. A JVC pj, on the other hand, can't do that. Although the black level should be the same in HDR mode, it's not on the JVC's. If you switch to High Lamp mode to see the brighter HDR highlights, that harms your black level. The fact that the JVC auto-iris is (mis)programmed to stay wide open for HDR content makes a fade to black look like you're watching an inexpensive LCD projector instead of a Brutal Contrast Monster.
HDR light levels reach 1000 nits or more, but how bright is a JVC pj? 70 nits is probably in the general ballpark (70 nits = 20 foot-lamberts). SDR content is graded for 100 nit displays, so how can you hope to accomodate 1000 nit HDR content on a 70 nit display?
Normally a JVC would be calibrated so that SDR content takes full advantage of the JVC's limited light output. If you send the JVC HDR imagery, it will lower the 100 nit white point to make room for the HDR highlights. That results in a dim image. If you try to make the image brighter by increasing the Contrast, you end up clipping more and more of those HDR highlights. The end result is that your average brightness is lower, you've clipped most of the HDR highlights, and your black level is poopy.
Given the problems that JVCs have displaying HDR content, I feel that sending it tone mapped SDR will offer the best image possible. Barring a tone mapping solution (eg. Radiance Pro), sending your JVC a clipped SDR image can still look excellent if the player's Contrast & Brightness settings are properly adjusted.