It should fire more or less instantly if you let the PGM-Fi light go out then turn to the start position.
Something else you could try before getting the compression tester out :
Add that to 1/4 tank or less of petrol - don't add any petrol just the meths as long as it's 1/4 tank or less. If the yellow "Feed Me" light is on, you could add a couple of gallons (9L in new money) but otherwise no more than a couple of litres just to flush it into the tank. Easiest way is with a fuel can, half full and add the meths to the can then add the entire contents of the can to the tank.
What i'm thinking is condensation in the tank, settles overnight at the bottom of the tank so it's pulling water through, makes cold starting tricky and gives an uneven idle.
I usually put a 2L bottle of meths through once a year on mine to keep the condensation at bay. It's better if i use it more regularly but if i don't, it tends to biuld up condensation more.
Something else i've found, 50ml (that's a pub double or about an egg cup full) of ATF in a full tank of petrol, preferably synthetic ATF, is amazing at cleaning injectors. I've tried it in my Volvo then because i was impressed with the results, tried it in the Sterling - even more impressive! Mentioned it to a few other people online, they tried it as well, one in a 760 Volvo similar to mine, the other in a J plate 820Si - all very good results.
For heavy duty injector cleaning, 50ml in half a tank works nicely! Do the meths first though, in case it is condensation.
If nonne of the above helps any then it's time to buy yourself a compression tester. I have one that you'd be welcome to borrow but with the cost of sending it to you then sending it back again, it would be almost as cheap for you to buy one then you'd have your own. I can explain how to do it, it's not just a case of remove a plug and screw it in, especially on the 827, there's a couple of other things to do as well. Needs to be done on a hot engine as well which is fun!