The convention of using "ABCDEF" didn't get established until well after the LGP-30 was designed in the 1950's. The Wikipedia entry on "Hexadecimal" says "The now-current notation using the letters A to F establishes itself as the de facto standard beginning in 1966, in the wake of the publication of the Fortran IV manual for IBM System/360, which (unlike earlier variants of Fortran) recognizes a standard for entering hexadecimal constants."
The comments elsewhere that note the layout of the Flexowriter character set risk conflating cause with effect. The single-character mnemonics for the sixteen hardware instructions were chosen by the LGP-30 designers to be, well, mnemonic; and then the remaining characters FGJKQW were left to represent the values ten through fifteen. This then forced the assignment of character positions for the Flexowriter device, so that no table lookup would be required when reading opcode mnemonics and also when reading hex numbers; all bits could just be shifted into place in both cases.
Trigger warning: The phrase we were taught was standard in the LGP community to help remember FGJKQW was, I'm afraid, "For Good Jokes, Kill Quiet Women." This seems to have been excised from the written lore fairly early on, as search engines have no record of it.
+----------------------------------------------+
| 00 20 40 60 00 20 40 60 | (1) triangle
+--------------------+ +--------------------+ (2) pi
| RE NL ST | 00 | RE NL ST | (3) sigma
| z i p h | 01 | Z I P H |
| 0 4 8 j | 02 | ) (1) (3) J | BS Back Space
| SP / o | 03 | SP ? O | COL COLor
| LC BS | 04 | LC BS | DEL DELete
| b d e c | 05 | B D E C | HT Horizontal Tab
| l 5 9 k | 06 | L % ( K | LC Lower Case
| - . x | 07 | _ ] X | NL New Line
| UC HT | 10 | UC HT | RE REad
| y n u a | 11 | Y N U A | SP SPace
| 2 6 f q | 12 | * $ F Q | ST STop
| + , | 13 | = [ | UC Upper Case
| COL | 14 | COL |
| r m t s | 15 | R M T S |
| 3 7 g w | 16 | " (2) G W |
| , v DEL | 17 | : V DEL |
+--------------------+ +--------------------+
| lower case upper case |
+----------------------------------------------+
Taking bits 2–5 gives you: 0 l 2 3 4 5 6 7 8 9 f g j k q w