Andy
If you mean the Mead family of Wendon Lofts, Essex, there is no connection to the Meads in Bucks. This was in a tract by Henry J. Mead, written in 1918, but he is mistaken. He has good information for the Meads in Soulbury in later generations, but the connection to Essex is nonexistent.
You can read it here:
https://sites.google.com/site/meadfamilyhistory/home/counties/bucksAs for the Meads in Bucks, you are mixing several families. The Richard Mead who died in Soulbury in 1643 was born there. His family had been living there since the 15th century.
Using wills, parish records, court records, etc, I have traced them, here:
https://sites.google.com/site/meadfamilyhistory/home/counties/bucks/soulburyThe wills are here:
https://sites.google.com/site/meadfamilyhistory/home/wills/bucks/willsParticularly the wills of William Meade 1558, James Mede 1558, Agnes Meade 1561, Richard Mead of Soulbury 1642/45, the inventory of his widow Joane 1670/1, and Matthew Meade in 1699.
Monks Risborough is more difficult, because there were Meads living there and in Princes Risborough, Saunderton and other nearby parishes since the 15th century. There were a lot of them.
In Monks Risborough, Richard was the son of William. The parish records:
Monks Risborough St Dunstan
28 Dec 1587 John son of William MEADE
8 May 1589 Elizabeth daughter of Wm MEEDE
6 Jun 1591 William son of Wm MEAD
25 Mar 1596 Richard son of William MEADE
14 May 1598 Henrie son of Wm MEAD
30 Jan 1603 Dorryty daughter of Wlm MEAD
William married in 1587:
Feb 1587 27 MEEDE William & BAMPTON Alis
And he died 1610:
25 Apr 1610 William? MEAD husband of Alis
Before that I can't be sure. There were Meads living there and nearby since 1400 if not before. No Poll Tax Returns (1377-81) survive for Bucks.
As for Amersham, that's probably another different family. There are parish records for Richard:
31 Oct 1636 John son of Richard & Catharine MEAD
1 Apr 1638 Mary daughter of Richard & Catharine MEAD, Carpenter
Before that there was a Thomas Meade in Amersham who had children between 1611 and 1621 but none named Richard.
So I guess the first thing to do is forget Ancestry.com and see what you really know based on real information from wills and parish records.
There is a service from the Bucks Family History Society where they provide all parish record extracts (baptisms, marriages, burials) for a 100 year period for one surname for 3 pounds each:
http://www.bucksfhs.org.uk/index.php/database-searchesI have them for 1538-1638, but not afterwards. That's where I got the parish information above.
My homepage:
https://sites.google.com/site/meadfamilyhistory/homeFrom there you can look at counties/Bucks and wills/bucks. The transcribed wills are in a subpage link at the bottom.
So I have to end with a question: who is the person you are sure about, based on contemporary information?