Of course, we retailers want and need to follow clients' orders. But we also have a responsibility to inform our clients about the hazards of their ill-advised requests. And if the client insists on destructive framing materials/methods, at some point we should say, "I'm sorry, but what you're asking is destructive to your valuable art and contrary to accepted practices, so I must decline the job".
I'll stand by my original suggestions: Glaze it and use a non-invasive, completely reversible mount. Fitting is important. Lining the rabbet with a gas-impermeable barrier is a good idea, and the frame should have a filled & covered back.
Oil paintings on canvas are intrinsically more durable than paintings on paper, and are more tolerant of environmental changes. Also, in a museum's carefully controlled environment, where handling is done by professionals, framing an oil painting on paper without glazing might be OK. But in a consumer's home or office? I wouldn't advise it.
Oil paintings don't need to breathe, according to CCI (Canadian Conservation Institute) and FACTS (Fine Art Care & Treatment Standards) Institute. If tightly closing the frame for an oil painting on paper would cause any problems, please explain them.
Slowing the rate of temperature and humidity changes is important for the paper. That's the purpose of glazing (with generous, insulating air gap) and filling (insulating) the back.
Yes, the oil paint will offgas, and closing the frame tightly would confine the painting's chemistry within the frame. But what would be the harm?
The offgassing would eventually fog up the inside of the glass. So every couple of years you disassemble it, clean & refit it. Periodic inspection & refitting is advisable for valuable artwork in any case. And over time, as the paint dries chemically, the offgassing would diminish.