Not definitive, no!
As far as LI caps go, although modern illustrations may suggest otherwise, there are still only a few reliable references for the AWI campaigns.
As mentioned in another thread, there is a useful article by the late Michael Barthorp in 'Military Illustrated' from October 1990, which summarises the best known forms of LI cap and the source material for 1770-1799.
For the AWI period, he discusses the '1771 Pattern Cap' (i.e Keppel); the various 'Minorca caps' worn by piquet companies existing before the 1770-71 formation of LI coys: the 11th & 25th (in style of short fur-trimmed grenadier caps) and the 13th (either a cut down 'cap-hat' or, IMHO, a folding 'bicorne' style); the peaked leather 'helmet cap' of the 5th (with frontlet and comb ornamented with brass furniture, red turban and horsehair crest; the rarely seen 'Lambton' cap of the 68th with highly decorated brass front and motto 'Faithfull', which was worn in the West Indies.
He also touches on the felt caps converted from hats ordered for all his infantry by Burgoyne in 1777 as illustrated by von Germann, together with discussion of the headgear of the LI coy of the 45th Regt (drafted & reformed in England 1778) mentioned in inspection reports of 1780 & 1781 as "more like the caps of the light dragoons"- whether the pre-war peakless neo-Classical helmets, or the new 'helmet caps we know as 'Tarletons'is not clear.
Barthorp does not discuss in detail the various LI caps as seen in Loutherbourg's paintings of the 1778 Warley Review but includes details of the artist's preparatory sketches, including views of a Keppel cap and 'cap-hat' (with frontal and turned-up back 'leaf) attributed to 6th and 69th Regts respectively, and a Militia officer's 'helmet cap' – a lighter version of the 5th's cap- with horsehair crests, standing 'hackle' plume and 'tyger skin' turban – (a militia officer speciality, it would seem).
Other than that, Barthorp only omits the 1781 portrait of Capt. Thomas Hewitt of the Tenth LI coy, holding his partially visible cap with narrow peak (visor)and plain front decorated only with a small star and regimental number (- which Mollo & McGregor illustrated more fully in their book on AWI uniforms). The Tenth were drafted in 1779 and reformed in England.
Coote's orderly book mentioning the 37th's crested felt cap had not come to light and the CMH research into the form of the Foot Guards cap had not been done at that time.
Don Troiani cites OB reference to a 'cap hat' provided for all of the 15th regiment on departing for America in 1775, with the LI coy probably dressed in similar fashion. His illustration in "Don Troiani's Soldiers in America, 1754-1865' shows a battalion man in a cap apparently based on the 'cap-hat' sketched by Loutherbourg in 1778, (i.e. with turned-up back 'leaf' although the angle doesn't show this).
DT has also opted for this style in his painting of the 3rd Buffs at Eutaw Springs, in immaculate caps bound with pristine white tape, presumably based on an OB reference as well. He has chosen to decorate the cap front with an atypical Dragon badge (more like a Wyvern), based on an item found on the battlefield, possibly from a cartouche pouch
AFIK, that about sums up the styles of LI caps for which we have evidence between 1770-81. There are one or two surviving Keppel caps in museums, together with the cap of the 5th and a similar item to the 9th (of uncertain provenance) both in in NAM, and the 'Lambton' cap, which is I know not where.
Links ( I hope ) to Barthorp/Turner illustrations
link