A good technical case could, it is true, be made for this on the grounds of the Bishop Graham Leonard precedent. But, in his case, the CDF considered the orthodoxy or otherwise of every 'link' in the ordinations which led from the Dutchmen to the Bishop who ordained him priest. It cannot be anything other than a profound mistake in practical terms to attempt to clutter up the beginning of an Ordinariate with the sort of paper chases and delays which would be involved. And it would create an invidious divide between most of us and a few worthy priests who, because of age or because they were ordained in other parts of the Anglican Communion, were priested by bishops who had not contracted the Dutch Touch. So, my strong conviction is: NO ... just don't go there.
But is there a problem in conscience about 'receiving again' the Sacrament of Order when one is morally certain that one has already received it? This did indeed trouble Blessed John Henry Newman. But he willingly accepted it after being assured that the conditionality would be "implied in the Church's intention" (Ker pp 321 and 466). In view of the repeated assurances given, to the effect that clergy entering into full communion are not being required to deny the validity of anything they have previously received or done, and the careful statement of Fr Aidan Nichols that the invalidity of Anglican Orders is not now unconditionally proposed by the Roman Magisterium, I feel that the understanding which satisfied Newman should be good enough for less brilliant minds than his. Indeed, if the Magisterium took the view that those entering an Ordinariate must accept the invalidity of their current Orders, either explicitly or constructively, they would presumably have required that, before even applying for admission to the presbyterate of the Latin Church, Anglican clergy should have ceased performing sacrilegious simulations of the Eucharist. This is, quite simply, not the line which, so I gather, has been or is being taken either in Rome or locally.
Trent did indeed say, as a correspondent reminds me, that three sacraments non possunt iterari. The present indicative of possunt demonstrates that this is simply a statement of fact. If "Ordination I" was valid, then "Ordination II" is as a matter of fact a nullity. If "Ordination II" is valid, then "Ordination I" must have been a nullity.
I do, however, have a preference about how things are 'done'. If Anglican priests were 'reordained' at a grand, public, triumphalist ceremony, this might have the body-language of "These men were not really priests before". And it could be extremely damaging to ecumenical relationships generally - something which Rome and - so they keep telling us - Westminster too, are rightly anxious to avoid. But if the proceedings were private and low-key (like the ordinations of Bishop Leonard and a number of others), the Anglican Establishment need not be offended, and the conviction of Anglicans that their priesthood truly began at their original Anglican ordination would be respected by the 'reordination's' social marginality and its lack of public ritual assertion. In 1993 Fr Aidan Nichols advocated proceeding along exactly these lines in his elegant picture of an Anglican place of study which could "provide supplementation for the priestly training of former Church of England clergymen and a discreet setting for the making good of any defects in their Orders".
A final dash of rhetoric. Forget for a moment the RC question; if I became an Orthodox, I would undoubtedly have to be 'reordained' in order to liturgise. Can it really be God's will that Catholic Anglican priests are boxed into a prison camp out which it is impossible for them in good conscience to move into the ministry of any of the Ancient Churches? Is the 'Consensus of the First Millennium', to which so many among us (especially the less 'papalist') have so often appealed, in fact permanently inaccessible to us?
Are some of my brethren sure that this particular 'difficulty' is anything other than a clutching at an arguably respectable pretext for 'not going'?