Given the evidence for the surname in Reaney and Wilson under Stallworthy, where it is stated the longer form is an altered form of stalworth, after worthy. That being the case, we should give the submitter his originally requested form of Stalworth.

Looking at the drawing in Foster, it seems to me likely that the blazon is happenstantial and this is just a fancy drawing of a cross bottony. Note that the drawings in Foster are not period drawings, they are 19th C. work by the author.

A bit more research proves confusing. Anglo-Norman Armory II, C. Humphery-Smith, p309 blazons the cross of John Benstede (from the Falkirk Roll) as ... a cross clechy voided and bottony argent (and each convex intersection of the cross clechy has a small trefoil attached!) Brault, in Eight Rolls of Arms, p89, gives the blazon from the Thevet version of the Falkirk Roll as "87. Sir John de Benestede port la croys perce' et patee et botonee d'argent." (There are no emblazons in Brault.) In the notes it says that the tincture of the field is missing in both copies of the roll. Looking at the rest of the roll the blazon is peculiar in several respects, not the least of which is the lack of field. If different authorities in different books have vastly different interpretations, enough to change the recorded blazon in the case of Cecil H-Smith, it seems to me that this is good evidence that this cross is a one-off period weirdness.