As has been said, you can do the modular route quicker then the integrated. Its possible to do the exams in 4 months if you work hard. It depends on whether you have the time and commitment to study around work and family etc. I did mine on the train to work and lunchtimes plus evenings and managed to juggle it around family etc. This also meant i was getting paid at the same time. It will also allow you to speed up or slow down the training around the market,
I know you have the funds but do you really want to be sat in some classroom and paying for it knowing you could be studying in your own timeframe probably quicker and getting paid at the same time.
Get your hours up either in the US or with a cheap share at the local flying club and enjoy the flying. Im always amazed at the number of people that say they really want to be a pilot but seem to view the real flying part of the training as some kind of obstacle to be overcome as quickly and cheaply as possible. This seems to be the way the integrated schools look at it as well. Whilst doing your hourbuilding you should fly as many types of aircraft and as many diffetent types of flying as you can. Get a tailwheel rating and do some grass stripping, maybe some aeros, get a cheap share and do some flying/camping around the uk and europe.
Despite some of the posts on here you do not need to spend all of your hourbuilding practising CPL standard flying. This is the time where you should be enjoying it and becoming comfortable in the air and making decisions. Maybe even scaring yourself a bit. This is what the hourbuilding is for, turning you from fresh PPL to commander of the aircraft. Leave the epaulettes for later and get involved in the local flying club. You will make better contacts here than you will at any integrated school. My local airfield is crawling with airline captains. There will also be opportunities that open up which you have not even thought of plus the chance to backseat and watch other more experioenced pilots.
The I/R CPL can be done relatively quickly and with the amount you have saved going modular plus the extra you have earnt whilst doing the exams could be used to pay for a TR if you get offered a job that requires it paying up front.
I dont see that you need to rule out anything in terms of long term career aspirations. You never know what jobs will present themselves in the future and as long as you willing to take the opportunities as and when they arise.
If I were you I would be booking my first PPL lesson and getting my class 1 medical if you haven't already.
Good luck.