Sounds like you might be going through 'manopause'

Your situation is not unusual or uncommon, and you have a range of options before you, some better than others. And you have seen the range of responses on this thread from men who wished they had what you have. So, let me humbly add a little bit of wisdom from this fool who neglected two marriages (and the sons from each).
You have an amazing wife and a great relationship. Be very grateful for that, as you have a wonderful place to begin the discussion.
Sit down with her and talk about where you are at, your needs and desires. Be gentle but honest. You love them; you don’t want to lose them, but have this need for something more. Be totally open and vulnerable with your wife about what you are struggling with, and have her join with you in working out the solution. It is not totally uncommon for wives to be understanding and to allow their men have a bit of variety now and then. I have a good friend who gets the freedom to go and chase some other tail once a year to fulfill any need for variety (though I don't think he has taken her up on it). If your wife feels totally secure and sees that this is just about sex, you never know what her response might be. I know this is kinda scary to be that open and vulnerable with her, but this is the kind of thing that if you have an amazing, loving wife you can work through together, and you could have an even more amazing and wonderful relationship as a result. She may also say no to you, but together you can find a solution together. It might mean going to a counsellor/therapist together to work through this. She might develop some role plays you can do to spice up your love life (could she play the role of a courtesan who you meet and wine and dine somewhere, and then go to a hotel for a wild night of sex)?
The drugs could be messing with your system. I am rather sceptical of the pharmaceutical industry as there is often potential for all kinds of nasty side effects, and there are other modalities and ways of addressing the problems.
Sir Lance alot said to “dig deep” and there is wisdom in that. You have the answers inside you, and maybe your hesitation is confirmation of that answer. Put aside your mind chatter and horniness and listen to your intuition and your inner voice.
And, having sex with an SP isn't necessarily that great. And I would be careful about the terminology you use in relation to any discussion about sex workers. Don't say 'prostitute.' Talk about sex professional or courtesan. Give the impression of high end and stick with that, as it is likely to be much safer. Position them as professional who help men in your position.
I don't know if there is something you could give your wife to read to help her understand, nor do I know what that might be. Some of the ladies on here might be able to suggest some reading material to help your wife understand the healing role that SP's can play. If your wife can recognize the difference between the physical (sex) and the emotional (the relationship), she might not be as threatened by the idea of you gaining some healing from other women.
Anyway, whatever you choose, all the best in it... but don't risk what you have.