Coins of Class 2a, are relatively scarce yet the varieties that exist suggest that there was some degree of experimentation before the more consistent forms of 2bi and 2bii were arrived at. This has made any form of analysis or breakdown into sub-groups extremely difficult. This article suggests a means of dividing class 2a into two parts and identifies two further sub-groups 2ab1 & 2ab2, which could be confused with the coins of class 2b but which may well predate the issue. The article concludes with a brief table of the details of the four types identified.
Henry III Long Cross Pennies – An Analysis of Class 2a and the Identification of Two Previously Unidentified Subgroups – Ian Heavisides
BNS Research Blog 
Ian, thanks for sharing the fruits of your research which appears targeted at serious students of the Henry III long cross coinage – I know you’ve been looking at a lot of coins for a very long time. This article of yours makes a lot of sense and explains why I’ve had trouble assigning a number of coins to either 2a or 2bi; the recognition of a transitional group, 2ab, is helpful.
With class 2a being introduced in mid-December 1247 and the provincial coins of 2bi commencing in the Spring of 1248, we are thus looking at a period of about 4 months for your types 2a1, 2a2, 2ab1 and 2ab2. If experimentation was proceeding at a fairly uniform rate then we would be looking at approximately one month for each of your four groups, though in my experience there are more 2a type coins in existence than the transitional 2ab type – so maybe the experimentation was more towards the end of this phase, with the transitional coins being produced from dies prepared over a matter of weeks rather than months. These transitional coins are relatively much scarcer than class 2a pennies, and worth looking out for.
People tend to be “splitters” or “lumpers”. I suspect the “splitters” will be happy with the increased resolution provided by your scheme, but for the “lumpers” this may be a step too far; personally, I’m happy to now think in terms of 2a, 2ab and then moving on to the 2b types, and I’m looking forward to seeing if you come up with anything new concerning 2bi & 2bii.