The only information I have found is from this web-site
Interestingly it seems to leave out the other two Hallifax named vicars, or at least those proposed in the pedigrees held at Suffolk Record Office.
This internet list is explicitly about the Rectors of Springthorpe while the Hallifax documents refer only to the vicars. I wonder if there might have been both over the period from 1621 to after 1686 so it might be instructive to make a list of these rectors and the supposed Hallifax vicars:
|1624-1643||Thomas Wye. 1624. By the Prince of Wales. First fruits 12 May 1624. [Called Thomas Wier. Still Rector 1642-3].||1621-1660||Reverend Robert Waterhouse Hallifax Vicar of this Parish from the year 1621 to 1660|
|1654-aft 1671||John Halifax. In 1654 and 1671. John Halifax had two sons in Orders. Of these, Thomas matriculated at Brasenose Coll. Oxon 1679, proceeded B.A. 1682 and M.A. 1686. He became Vicar of Streatley, Berks 1693, and rector of Compton Bassett, Wilts in 1710. The other son, William Halifax, matriculated Brasenose Coll. Oxon 1671, became Scolar of Corpus Christi Coll. 1674, B.A 1675, M.A. 1679, Fellow 1682, B.D 1687 and D.D. 1695. He was Chaplin to the British Factory at Aleppo 1688 - 1695, Chaplain to the Spea|
|1676 on||Thomas Mason. 1576. B.A. By King Charles II, on death of last incumbent 22 Mar 1676. [Ordained priest by Abp of York 1674].||1686 on||Thomas Hallifax M A July the 7th 1686 of Brazenose College in Oxford Vicar of Springthorpe in the County of Lincoln|
|1705-1717||Thomas Reynolds. 1705 - 1717. M.A. By Queen Anne 10 Jan 1705. [Ordained priest by Abp of York 1679. Also Vicar of Haugham].|
|The notable thing in the above table is that the information from the rectors' site precisely agrees with that in Alumni Oxoniensis.|