1. The whole point of having low latency is so that we can use some fx whiled owing record-monitoring.

2. There are also times when I want to record the actual fx so I'll arrange setting up my sound outside the box.

Generally I like to do 1 in preference to 2.

FreeFlyBertl

AT
Use an amp?

Anyone still doing that these days ???? ;-)

Sure we do - but using a Radial JDX over reactive speaker load rather than miked.
Could be used in any apartment too, if needed to - dead silent(but phone leakage).
 
4 different amps through a patch bay, so I can run any preamp into another power amp.
And a pedal board with various tube driven compressors and the usuall stuff like parametric EQ to decide exactly which frequencies saturate tube stage first.
 
And a range of guitars to go with it.
 
Isn't anybody serious about guitar tone these days....

There should be an answer to this, I have what might be considered an underpowered processor nowadays, a Q6600 quadcore, but have never had a problem recording GR4 or now 5 using input echo on low buffers. I tend to agree with a few others in here, that perhaps the latency on some other fx may be stacking up the problem. With an i5, a decent audio interface and the correct drivers, you should be good to go. Think about it, your ASIO control is showing low latency, (mine is 3ms and 12ms round trip which is almost double yours at 6.2ms ) so I believe there really is an ITB fix to this for you to find.