You might be interested to know that you can find the St Nicholas Church Strood Parish Registers online at the website (cityark) cityark.medway.gov.uk.
Once in the site chose Medway Ancestors from the Lefthand blue box.
The register images are difficult to read and don't contain mother's names.
I have gleaned the following Ewers of Strood (There may be more). The jpg names refer to the image file on the website for the particular page of the register, and the years are the years that particular file covers:
ursula ewer (00000016.jpg) 1586-9 thomas ewer (00000018.jpg) 1591-4
elizabeth of thomas ewer (00000029.jpg) 1618-20 robert of thomas ewer (00000031.jpg) 1622-24 john of thomas ewer (00000032.jpg) 1624-26 sara of thomas ewer ((00000034.jpg) 1629-30 elizabeth of thomas ewer ((00000035.jpg) 1631-32
mary of philemon ewer ((00000030.jpg) 1620-22 thomas of philemon ewer (00000032.jpg) 1624-26 sara of philemon ewer ((00000033.jpg) 1627-28 william of philemon ewer ((00000036.jpg) 1633-34
bartholemew? cobden & ursula ewer (00000079.jpg) 1612-16 thomas ewer & bridget hipsley(00000079.jpg) 1612-16 humphrey? mottershed & elizabeth ewer (00000080.jpg) 1617-24 william ewer & mary dann (00000083.jpg) 1635-39
elizabeth of thomas ewer (00000058.jpg) 1617-19 robert of thomas ewer (00000058.jpg) 1617-19 robert of thomas ewer (00000060.jpg) 1622-24 bridgett (wife) of thomas ewer (00000060.jpg) 1622-24
Incidentally there is a probate document which is an inventory of a tailor's shop of Philemon Ewer of Strood in the UK National Archives (from I think 1660). From the Strood parish registers i would guesss that he was Thomas Ewer's brother and the shop maybe where Thomas worked prior to going to America (He was a tailor I believe).
The website is www.nationalarchives.gov.uk and the reference number of this probate document is PROB 4/6825 (224229).