I feel like this is probably a "duh" answer but it eludes me.

I have a flagpole mount for my hitch receiver.  It occurs to me I could use it to support my fishing pole, but it would be too close to t u e operating position to rig tye antenna as a sloper.  Maybe I could do an inverted L.  

But with much of the wire now rigged vertically, does that mean it will need radials?  It seems to work without radials when set up as a mostly horizontal sloper.

No, not needed, but they may help alleviate ground losses and make it perform better.

I like running the EFHW vertical when I can get a nice tall branch to hoist on and get the feedpoint up about 8 feet from the ground.

Typical direct-feed verticals are 1/4-wave elements, so they need the radials to act as the other half of the antenna.

Well that's good to know!  I guess the next question is what's the radiation pattern look like?

On the primary band it's cut for, mostly broadside to the wire but up-angle a bit if it's close to the ground, so sort of like a regular 1/4-wave vertical, lower to the horizon and omni-directional.  It's basically the same as a vertical dipole there.

On the harmonic bands, it gets lobey, and it depends, some of them end up with the highest gain lobe pretty high angle, so not as good for further DX, but it's still omni-directional which is nice.

I'm going to disagree!

An EFHW is nothing like a dipole, vertical or otherwise. It is a half wave monopole antenna by definition. The balun is only an impedance match for all of the bands it is not resonant on. Put it vertically you have a half wave vertical. Bend the top over as an L and it's still nominally a vertical.

Vertical antennas need radials for best performance. So do inverted L's.

Does this mean you shouldn't run it without radials, or that you won't get some performance out of it that way? No. Hell, I run an inverted L with only two elevated radials, I should really have 4. Everything in life is a cost/convenience/performance trade-off. But, on paper, in theory, the "right" way to do it is to have radials.

One day I'd like to take the time to set one up and do real world tests with and without radials, take field strength readings and do propagation comparisons with WSPR, etc.
But in modeling software, there's not much of a difference.  This doesn't account well for real-world ground conditions, but it's at least some theory to start with.

That is interesting.  It looks like the no radial, end fed version has slightly better gain and SWR vs the one with radials and the center fed vertical dipole. (If I am reading these correctly.)

Why did you choose 3 meters above ground?  Is this a guess based on ground conductivity for a surface mounted antenna?

IMO, all EFHW antennas need at least a counterpoise or the coax shield will become the counterpoise no matter what orientation it has. The only difference orientation makes is how much the ground losses are. A low horizontal EFHW will have high ground losses so the lack of a counterpoise will make less of a difference in efficiency. When you orient it vertically / Inverted L or raise the horizontal much higher, you now have the potential for a lot less ground loss IF you have a good counterpoise / radial field and when you don’t, the lack of efficiency / poor SWR is more noticeable than a low horizontal orientation where you have big ground losses no matter what you do.

The inside of the coax shield has signal on it and that signal needs a 50 ohm radiator ( just like every other antenna ) or you will get common mode on the outside of the shield and an inefficient antenna ( and less than ideal impedance / SWR ) due to a poor match, even with a balun or match transformer.