I'm clutching at straws on this, but until someone who knows what they are talking about comes along, I thought I'd ask you the questions that I would ask myself in such a situation.
Relevant thoughts which led to the questions.
The bike does surge if you start to ride it before it is properly warmed up. Probably due to the action of the wax unit making adjustments as the wax melts.
I was told by a respected Honda mechanic that the ECU adjusts according to the way it is ridden. No one on this forum has been able to confirm this - but the notion is that if it is ridden without a great deal of throttle input, then the first time you apply the throttle it can hesitate and it needs a couple of blips to make the ECU realise it has got someone demanding a bit more excitement in control of it. I've experienced this sort of behaviour a few times after long stints on dual carriageway and the engine faltering after slowing down and wanting to pick up speed - then whooshing in the power after a couple of blips of the throttle.
When my HT system (plugs and leads) started to fail, the symptoms were initially a slightly bumpy ride - nothing more than a feeling of riding along a tar and gravel road surface. Later a reluctance to accelerate until the revs picked up and then it would take off as if nothing was wrong, particularly noticeable when the gradient increases and it is expected to do more work without actually increasing the revs. Finally a reluctance to do anything unless the revs were held high.
Part of your description reminded me of the first two phases. My explanation was that the spark was not strong enough at normal riding speeds. When the revs were higher, the electrical output increases and the 'spark' becomes strong enough to jump the problems in the HT lead.
The Mice thing is a real issue, but not necessarily to do with what you describe. However, the throttle cable acts on a pulley wheel which is under the airbox at the front. One cable pulls the intake butterflies open. The other cable pulls them closed. A cable with no free play in it can cause issues - because all such mechanisms have their tight spot, and the inner cable tightness is affect by the position of the steering. Too much slack can make it difficult for the rider to respond to the engine's demands.
Any debris down there may (possibly) affect the movement of the pulley or of the mechanisms opening / closing the intake butterflies. If something like this is the cause, then this really would be clutching at straw.
But I wouldn't start diving in to these suggestions until others that may recognise the symptoms have had chance to contribute - but your answers may give them more useful information to work with.
One thought. Put some injector fuel cleaner in the tank. Fill up with some high octane, low ethanol fuel. Give the bike a treat and go for a long ride with plenty of variety, accelerating and decelerating. Keep the engine revs higher than normal - use a gear or two lower than normal - say about 4k-5k rpm.
At some point between 3/4 and an hour the engine will probably loosen up and feel to be spinning more freely. That sounds very vague, but you will feel it and you will know when a stupid grin comes onto your face each time you open the throttle.
I did it with mine (without thinking about it really) on Monday when I went for a short run which ended up as 244 miles. Mid afternoon I had an empty road with lots of twists and turns and climbing - and I got the stupid grin. Oh yes - I'd forgotten about that.
But bear in mind that you don't yet know what is happening in the engine - so depending on how you feel about the engine may determine whether you do this now or later. But if you do it now be wary - keep your hand ready on the clutch, for example.
Others may chime in talking about fuel pumps and 5 way tees, air filters and fuel filters - which may suggest doing a bit of work first.
