Yes there can be phase issues with a single source. Look at an on board acoustic guitar preamp sometime…see the phase switches on them? It makes a difference in both directions sitting there playing by yourself thru a pa/amplifier. They only have one pickup in most of those guitars too, so its not changing pickup phase. One way has alot more low end than the other. Kinda like reversing the hot and ground on a speaker. One way makes the speaker move forward and other it goes back on the initial transient.
I get that different loads sound different. I have three different ones, PS-2, Hotplate and Rocktron Juice Extractor. Not night and day difference but there is. I only have one amp with a line out, have never tried it so can’t comment on that. You must have some phase issue going on somewhere in your signal chain with the Suhr, your symptoms sure sound like one.
With the Hotplate, the tone switches work backwards when using it on load vs the attenuated modes. Always thought that was odd.
A mono signal CANNOT have phase cancelation within itself. There has to be at least 2 signals from the same source for there to be any potential phase misalignment.
I don't know about acoustic pickups... there must be something within them that has a potential, but once the sound is a mono signal in a wire or a mono track in a DAW, it doesn't matter if the phase is 0°, 180°, 73°, or any variance... it simply cannot be out of phase with itself. You can reverse the speaker terminals and the speaker moves in before out, and as long as it's the only speaker (or all the speakers have inverted terminals), it will sound exactly the same as it does when the terminals are the right way. The only way phase cancelation can happen is if there are speakers with different polarity, or if you have 2+ speakers mic'd with different mics/positions/distances, then each track can have slight phase offsets that will cause some cancelation. Or if you mic a speaker and send the line out directly, those are pretty much always out of alignment.
When you have one amp connected to one Suhr RL with the line out into one input/one track in the DAW, there is absolutely NO possibility of any phase issues. And plugging a speaker into the Thru jack is NOT going to change the phase of the line out. But even if it did, it would have absolutely NO effect on the sound in a mono track.
The difference in sound of the line out between the internal load and a speaker load has absolutely nothing to do with phase. I have a phase aligner plugin... I can shift the phase of a mono track by any number of samples and the sound will never change, it will only introduce latency when the shift gets larger than 100 samples. And the latency/phase shift can ONLY cause phase cancelation if there is another track from the same source being mixed with it.
It's just the way the SRL sounds. It sounds like that in demos/comparisons, too. I do actually like a thumpy, scooped, chuggy high gain sound, but it is terrible in a mix: fhe bass gets muddied up with the actual bass and the high end screech is all that cuts thru. You need the mids to cut thru a mix, and you need to roll off the bass. Bass-heavy and mid-scooped sounds good when you're just playing guitar by itself, but in a mix or with a band, you need the mids to be prominent.
I've been an audio engineer for 26 years, I know how things work and I know all about phase and the effect it has on interacting signals. The phase of a solo mono signal has absolutely no effect on the sound, and the way the SRL sounds has nothing at all to do with phase. I don't know what the deal is with the acoustic you mentioned (and I never will because I'll never have an acoustic guitar, I can't stand them), but I know for absolute 100% certain that a mono signal cannot be out of phase with itself.