I’ve been trying to do the same, I think there’s a certain about of enforced limitations with it – the various providers will say they sync with each other to help sales and they do to a certain extent, but they’d all prefer you used their device/app. For example I don’t think it’s possible to use the Fitbit HR’s HRM as your HRM for Strava and whilst you can sync your Fitbit data with MFP, it only acts as a pedometer, it doesn’t feed in your actual calories burnt which the HR fitbits do much better which is a shame because whilst the FItbit app can record food intake etc it’s not nearly as good as MFP.
I’m going to use the Fitbit app for everything as the HR is very good as actually recording calories burnt, better than MFP that really just records steps or Strava which doesn’t take into account terrain, bike type etc – 10 miles on a roadbike on tarmac or 10 miles over rocks and through mud on a fat tyres MTB same effort as far as Strava is concerned (like for like elevation).