You'd need a fairly quick-witted general at the had of the junta to be able:
1. to keep the royalist generals still in the country 'on side' so they didn't attempt a coup (which would cause civil war and their probable destruction but some might still try it to save the monarchy and their own role from the radical Islamic leadership)
2. to persuade the pro-Khomeini leadership in Tehran (based on the local mosques and the 'underground') of the crowds on the 'streets' that their sort of Islamic nationalist state was coming soon and they need not arrange any more open attacks on the govt. The latter would demand all the exiles being allowed back as essential to their plans.
3. to persuade Khomeini and his circle in exile in France to rein in the crowds for a while and see how the new regime developed - but this would entail having to let the exiles back into the country so they can organise there and put on more pressure. Probably Khomeini would then head to Qum as safer than Tehran for him, and surround himself with his armed allies there.
Even a 'mysterious accident' to Khomeini once he is back in Iran, arranged by royalists, will lead to more confrontation and a 'martyr cult' of him with allegations that the US was behind it - and probably a situation like the takeover of the US embassy in OTL Nov 1979 unless the military govt is prepared to risk a bloodbath. The mosques and students in Tehran will have less access to guns than in OTL 1979 as they have not disarmed the army and seized the artillery/ ammo depots, but they will still have a major presence from numbers and organization alone - an equivalent of the 'sections' in early 1790s Paris or the local workers soviets in 1917 St Petersburg. (I was fascinated by the parallels here as the events were going on in 1979, when I was a student.) I don't see the army and its leadership having the cohesion to 'do a Napoleon' and disperse the crowds with a 'whiff of grapeshot' as in Paris 1795, not least as the Shah had carefully avoided building up any powerful or prestigious general who could overthrow him in the 1960s or 1970s.
To keep any degree of cohesion, a general as the 'front man' for a junta that is ruling in place of an exiled monarch but is facing its own (more radical?) junior officers plus a large and menacing popular grouping on the streets needs a well-respected and publicly nationalist leader, even if he's pushed aside later - like General Neguib in Egypt in 1952-4 after their revolution, ie ruling as 'regent' for a new young monarch (in Egypt, an infant; in Iran, probably the Shah's teenage son if the Shah is persuaded to 'abdicate' after his flight on health grounds and let a new monarch take over) at the head of a nervous army junta . I agree that nationalising the oil industry and probably some other populist measures to seize the wealth of conspicuous and unpopular rich businessmen is probably vital to appease the crowds and egalitarian Islamists - and with the latter able to organise via local committees (SAVAK will have to be broken up) the latter will win any later popular elections. Cancelling the elections as it becomes apparent that the wrong people have won will end up like Algeria in 1994 - and is the army coherent enough to hold out and set up an oligarchy backed by scared secular politicians or not?
But there were other senior Ayatollahs, often older and more experienced than Khomeini (some over 80) in the hierarchic world of the seminaries of Qum, and also regionally powerful ones like Shariat-Madari in S Azerbaijan (Tabriz) and liberal younger men like Telagani; if they can be brought alongside to participate in politics and back their own allies in a more moderate if still Islamic-aligned bloc of support for the regime and Khomeini is blocked from the airwaves and kept in Qum, then his hard-line allies in Tehran (the fledgling IRP group) led by Ayatollah Beheshti might well not have a majority in parliament . You could get a restoration of the 1906 constitution with 'supervision' and 'ensuring that all legislation and MPs are fully Islamic' run by a grouping of senior clerics, not just Khomeini as 'Supreme Leader', no 'Islamic Guide' but a group of guides, and a collective leadership of Ayatollahs who in practice are weaker than not directing the govt. You then have the question of whether the hard-line and coherent Islamic radicals take over by force via their own coup (as Lenin did in Russia in Nov 1917, ousting a weak civilian Provisional Govt whose leaders had been too afraid of the army to let them fully loose on the radicals) , or overwhelm the moderates as 'more patriotic' and 'better organised with clearer goals' as Danton and Robespierre did in France in 1792-3. If Saddam invades to retake land, perhaps invited by alarmed generals as a republic is declared, then the radicals can play the patriotic card.
So we have choices - the road of Egypt 1954-6 (radical junior officers take over), Algeria 1994, France 1792-3, or Russia 1917. The clergy are stronger than in any of these, but can they be kept disunited or are the generals and junior officers too disorganised or too keen to save themselves to try it? Would some moderate generals 'do a Brusilov' and work for the Islamic leadership if the enemy invaded, or align with Bani Sadr's Islamic republican liberals to keep the IRP as bay and just offer a formal but not that 'hands-on' role to Khomeini?