I would need some convincing that Thomas Cranmer would have agreed with the 1662 revision as it seems to me that it sets in stone some confusion after the disjuncture of the Commonwealth period.
King Charles had the Scottish bishops and Archbishop Laud produce a Book of Common Prayer for Scotland (1637). This was a revision of BCP 1604/1559/1552. The revisions were often minor. It was this book, not 1662 (obviously!) which Samuel Seabury returned with to America, having been made bishop in 1784 in Scotland. You can find the text of the 1637 Scottish BCP here.
Here is the 1764 revised Scottish Communion Office.
This is nearly identical to Bishop Samuel Seabury’s Communion Office that he used as Bishop of Connecticut.
The 1637 Scottish BCP avoided some of the more obvious 1662 confusions. One of the more significant differences is that it had a proper Eucharistic Prayer:
The Presbyter shall proceed, saying,
Lift up your hearts.
We lift them up unto the Lord.
Let us give thanks unto our Lord God.
It is meet and right so to do.
It is very meet, right, and our bounden duty, that we should at all times, and in all places, give thanks unto thee; O Lord, holy Father, Almighty, everlasting God.
Here shall follow the proper Preface, according to the time, if there be any especially appointed; or else immediately shall follow:
THEREFORE with Angels and Archangels, and with all the company of heaven, we laud and magnify thy glorious Name; evermore praising thee, and saying, Holy, holy, holy, Lord God of hosts, heaven and earth are full of thy glory; Glory be to thee, O Lord, most high.
Then the Presbyter standing up, shall say the Prayer of consecration, as followeth, but then during the time of consecration, he shall stand at such a part of the holy Table, where he may with the more ease and decency use both his hands.
ALMIGHTY GOD, our heavenly Father, which of thy tender mercy didst give thy only Son Jesus Christ to suffer death upon the Cross for our redemption, who made there (by his one oblation of himself once offered) a full, perfect, and sufficient sacrifice, oblation, and satisfaction for the sins of the whole world, and did institute, and in his holy gospel command us to continue a perpetual memory of that his precious death and sacrifice, until his coming again; Hear us, O merciful Father, we most humbly beseech thee; and of thy almighty goodness vouchsafe so to bless and sanctify with thy word and holy Spirit these thy gifts and creatures of bread and wine, that they may be unto us the body and blood of thy most dearly beloved Son; so that we receiving them according to thy Son our Saviour Jesus Christ’s holy institution, in remembrance of his death and passion, may be partakers of the same his most blessed body and blood:
Who in the night that he was betrayed, took bread, and
when he had given thanks, he brake it, and gave it to his
disciples, saying, Take, eat, this is my body, which
is given for you; do this in remembrance of me.
At these words (took bread) the
Presbyter that officiates is to
take the Paten in his hand.
Likewise after supper he took the cup, and when he had
given thanks, he gave it to them, saying, Drink ye all
of this, for this is my blood of the new testament, which
is shed for you, and for many, for the remission of sins:
do this as oft as ye shall drink it in remembrance of me.
At these words (took the cup) he is
to take the chalice in his hand,
and lay his hand upon so much,
be it in the chalice or flagons,
as he intends to consecrate.
Immediately after shall be said this memorial or prayer of oblation, as followeth.
WHEREFORE, O Lord and heavenly Father, according to the institution of thy dearly beloved Son our Saviour Jesu Christ, we thy humble servants do celebrate and make here before thine divine Majesty, with these thy holy gifts, the memorial which thy Son hath willed us to make, having in remembrance his blessed passion, mighty resurrection, and glorious ascension, rendering unto thee most hearty thanks for the innumerable benefits procured unto us by the same. And we entirely desire thy Fatherly goodness, mercifully to accept this our sacrifice of praise and thanksgiving, most humbly beseeching thee to grant, that by the merits and death of thy Son Jesus Christ, and through faith in his Blood, we (and all thy whole Church) may obtain remission of our sins, and all other benefits of his passion. And here we offer and present unto thee, O Lord, ourselves, our souls and bodies, to be a reasonable, holy, and lively sacrifice unto thee, humbly beseeching thee, that whosoever shall be partakers of this holy Communion, may worthily receive the most precious body and blood of thy Son Jesus Christ, and be fulfilled with thy grace and heavenly benediction, and made one body with him, that he may dwell in them, and they in him. And although we be unworthy, through our manifold sins, to offer unto thee any sacrifice: yet we beseech thee to accept this our bounden duty and service, not weighing our merits, but pardoning our offences, through Jesus Christ our Lord; by whom, and with whom, in the unity of the Holy Ghost, all honour and glory be unto thee, O Father Almighty, world without end. Amen.