I would listen to your private specialist who is treating you as an individual rather than the arbitrary "computer says no" one size fits all NHS policy of discouraging oral estrogen after 60, as if it is perfectly safe at 59 years and 11 months then turns lethal at midnight on your birthday.
Studies showing an increased clot risk with oral estrogens generally looked at premarin or ethinylestradiol, not 17 beta estradiol, and these estrogens were often paired with a thrombogenic progestin. Doses in that era were also significantly higher, and far more people smoked.
This has not been conclusively demonstrated with natural estradiol in oral form either alone or with natural progesterone.
Many providers do not understand the difference between these oral estrogens or that the progestogen component also influences clot risk, and even in the worst case scenario assuming the risk is increased, they could not accurately describe its magnitude (which is in the order of one extra clot per several thousand women taking the absolute worst combination of equine estrogen and provera, for a whole year).
Even Louise Newson who is evangelical about transdermal estradiol has also recently stated publicly that any thrombotic risk is not really seen with oral 17 beta estradiol.