VP,
I can't give you any information about flying with high BP, but your tale rang so many bells for me!
Like you I exercise regularly, "drink in moderation, don't smoke, eat healthily and don't have any family history of high blood pressure and feel fit and healthy".
I had a heart "scare" in 2000, aged 37, being kept in hospital for 4 days under 24-hr observation while loads of tests were done. This was all down to an unusual ECG when admitted.
Upshot was a stress-test (treadmill + ECG), which was fine, then a discharge and a referral to a cardiologist (fine), and a battle to get my class 2 medical - again down to the unusual ECG (I've got some inherited oddity, that is perfectly healthy but non-standard). Finally sorted after several letters to Gatwick from GP and consultant.
All the above was, apparently, stress-related. No heart problem at all (the cardiologist even told me I had more chance of winning the lottery than having a heart attack in the next 10 years).
Four years later, a very stressful period at work resulted in me seeing my GP, who noted very high BP - I can't remember the figure, but it was sufficient to cause concern.
Like you, I had a 24-hr monitor (a bit weird, and rather hard to sleep), but it showed - happily - perfectly normal resting BP.
The point of all this is to show you just how much of an effect stress can have, and that it is perfectly possible that what you are experiencing is purely down to stress, and - literally - nothing to worry about.
The 24-hr monitor will - hopefully - give you a clear-cut indication, either no problem or genuine high BP.
If it's no problem- as it probably will be - you have to believe it, and concentrate on finding out about de-stressing and relaxation.
FBW