Troubleshooting a new shifter I'm trying to troubleshoot a new rear shifter that my bike store installed. The new shifter is a Shimano EF65, 9 speed. The bike is a 2016 Trek Allant 7.4D. I don't know what the derailleur is off hand and the bike is back at the shop at the moment, it's definitely a shimano 9 speed.

The 1st time I picked the bike up after having the new shifter installed there were about 3 bands across the entire range where shifting up OR down did nothing in terms of which cog the chain was on, they were more or less dead spots.

The 2nd time I picked it up after having it adjusted I had to shift down 2x then up once to get it to go down one gear: shifting down one time did basically nothing. Sometimes I thought it'd be in gear and then there'd be a massive *crunch* while on full power as it slipped down into the gear I'd actually selected. This nearly threw me once or twice.

The 3rd time I picked it up the downshifting problems were limited more to the upper gears (i think). 7 -> 6 would take about 200m of pedalling before the chain would eventually clunk over so I still have to downshift twice then up once to make sure I'm properly in gear.

Before I dropped it off it was shifting fine except for the 10 minutes before the original shifter failed. For a moment it randomly wouldn't shift down every now &amp; then, then it wouldn't shift down at all - there was 100% play, like the down shift lever was just gliding with no resistance. I tried to limp it to the store but about 10 minutes after getting stuck in top gear the bottom of the shifter fell off onto the road and the inner workings spilled everywhere.
Apart from that... it was running like a Swiss watch. It's been given a thorough service less than 3 months ago.

I think everyone's a bit confused at the moment. Are all shimano shifters for the same speed compatible? Is there a chance my derailleur could have worn along with the shifter so they'd be compatible with each other but not with a new drop-in replacement? What else could really have gone wrong? The hub's been inspected to see if the gears are indexing properly and apparently that's not the problem. I'm scratching my head a bit at the moment trying to figure out what could be wrong. We've spent about a month working on it so far and we haven't had much success getting it back to the way it was working before the original shifter failed.

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Update as of 15th May:

The mechanic tried a spare derailleur. He installed new Alivio cassette. He replaced the inner core of the shifter cable with a SRAM core, as he mentioned it looked as though the old core was snagging. He replaced the shifters with another set of Alivios.

Every single time I've picked the bike up from the shop the guys have told me it's been tested and is running fine. I don't doubt that they're telling the truth. I had one good ride to the shops taking about 45 minutes with panniers on and didn't experience the problem that one time. I usually ride for 1 to 1.5 hrs and every other ride, apart from that one good trip, I have experienced the problems a few times during the ride. This may be completely coincidental but I think I noticed the problems more frequently in the cold.

I'm wondering if the crunch / free spinning / lack of resistance on the crank sensation could be the freewheel, and the slow shift times might be a separate problem? The crunching seems to be set off most often when I shift from 7-8 but it also happens on bumps &amp; spontaneously a bit.

Last time I rode the bike I had time to start my helmet camera once the gear had already stuck, and recorded and additional 30 seconds of me shifting up &amp; down without the derailleur engaging the lower gear. 
                
              Hopefully you can see from the video which gear is stuck at the time, or any other detail that might be relevant.

Thanks in advance for your help!
I would start by looking at the shift cable and housing. The housing may be flexing too much and the cable may be sticking in the housing. This causes cable movement at the shifter to not be reproduced at the derailleur. If you are replacing the shifter it's a good idea to replace the cable and housing at the same time.   

Assuming you have a 2016 Allant 7.4. That bike came with 9 speed Acera shifters and a Deore rear derailleur. The EF65 shifter is a Tourney level component - that's at the bottom of the Shimano hierarchy. That may also be contributing to the problem. I definitely recommend going with a better shifter that matches the rest of the drivetrain.    

If your bike repair shop has spent a month trying to get this right with no success I'd also consider trying a different shop.