First, youre a great mom!
I think what youre doing is absolutely correct. Cutting off or throwing out an addict is often a 50-50 shot or worse. Its so much easier to get through such things with family and people you can talk to and lean on. Feeling rejected and sad, an addict will quickly turn back to drugs to lift his spirits if hes thrown out. It doesnt matter if he has no money, at least for a while, one always finds some. If its an illegal source, then that might mean getting a record which just ruins so many future options. Hard love can pay off sure but it is an extremely sensitive and circumstantial thing to pursue with an addict and unless youre absolutely certain about what youre doing I wouldnt try it. Especially in your case at this stage.
About money, I agree with you. Its necessary you dole out his money and check expenses. But dont (as with most things) or at least try not to do it with an angry, nonconditional approach. What I mean is, talk to him about it so he knows youre doing it because you care and you want to find the best solution for him together with him and his suggestions (and in general, one of the most important things with addicts is to be NONjudgemental, the moment he feels like youre looking at him sideways or constantly judging him whether he is good or bad etc.. he will feel the need to hide things from you, omit things in conversation etc.. Drugs are so prevalent in todays society, it can happen to our loved ones so fast, you never know how bad its gonna be and trust me that he doesnt really want to be an addict). This might not work with many kids, if theyre rebelious or unexperienced or angry etc.. But your kid is a college educated kid, I assume he will comprehend how this is best for him and listen to reason. So make him agree with you, this is the best way, ask him whether he has a better option and so on(have arguments prepared). But if you think he might not, that he might behave angry or he might feel trapped and pushed in a corner and you cannot turn it around, them you might need to be a bit more agressive with your suggestions.
Also the thing with subox. or any drug is that after a while, its difficult to function without it. So its great that you have a conservative doc. in that aspect, the best option here is definitely for him to go on a limited program. How long depends a lot on him, until he feels comfortable and doesnt crave (opiates I assume) anymore. One problem I often notice with subox. programs is that doctors have no idea how high a dosage is correct and overprescribe 10x over the dose. But I think with a conservative doc. that wont be the case hopefully.
And also, in my opinion and I think many others, one of the very problematic things is free time with regards to addiction. You need to keep his schedule busy. Free time is great if youre around him or if you know what hes doing. Too much thinking in these early stage too often leads to thinking how great it would feel. Just a little bit. Time can move so slow when youre getting sober. And then the rationalization begins. Try to make him to hang out with friends, the ones that dont use drugs. I know that is difficult to know but moms have a great instinct(Id trust it if I were you) about who is good or bad for their kid. If you dont know them, ask him about it, in these early stages if nothing else, he might still be remorseful enough to tell you with complete honesty about them

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Also spend time with him as a family. Have fun together. And like others have said, exercise. Lots and lots of exercise if possible, it works marvels on the brain and getting the brain chemistry back into balance.
And do please come back and ask further questions if you feel the need, its why this is here basically ?
and just love your kid and be nice with him, trust me he will respond better and feel a lot worse if he does sth stupid in comparison if youre angry and judgemental, then he might do it out of spite or anger or it just might serve his rationalization in some way why to relapse.
good luck