Part time or not ? FAA conversion ? Glass or not ?
Only the smaller schools (Wycombe, Stapleford etc.) will welcome you as a part timer - the Oxfords of this world are suited to catering for large numbers of full time trainees rather than caring for individuals.
If your part time is "weekends only" it's going to take a long time - three or four days a week would be much better. The IR really needs your full attention and effort. Many people need a lot of concentration at the end of the course to get that last step up to "exam pass level".
I would NOT recommend getting a FAA IR and then converting. Supposedly the conversion is 15 hours. You'll probably find that 25 is more like it - and possibly more - so how much would you save really ?. The folks I've trained with FAA licences have learnt in a very different environment. The things they struggled with were - NDB holds and approaches (almost extinct in the USA) ; Procedural approaches (lots of places in Europe have no radar so can't vector you - so fly the plate !) ; radio - VERY different in the US.
Timing - if full time - the quickest IR I ever taught was 5 weeks. Allow 7 or 8, more in winter.
Glass or analogue ? - Depends what you're going to do with your IR - if you're "straight to jets" glass is great. If your first post IR job is air taxy in a 30 year old Seneca and all you've done is glass - then you're probably going to suffer !. Flying glass is easier - as long as you can manage the technology !