Format of BBC Radio 4 .m4a files

[RS]

Does anyone know what software the BBC uses to encode its .m4a files?  I am 
unable to play them on an AGPtek Longevity player, which says it supports 
AAC-LC.  If I let get_iplayer default to flashaacstd, I get .m4a files with 
a bit rate of 128kbit/s and a sample rate of 44.1kHz or 48kHz (depending on 
the programme).  If I play them in VLC and look at Tools Codec no AAC 
extensions are shown, so they must be AAC-LC files.  Anyway this forum 
thread says an AAC-LC player should ignore SBR and PS information in HE-AAC 
files.
http://www.hydrogenaud.io/forums/index.php?showtopic=100252
If I try to play the BBC Radio 4 .m4a files in the Longevity player the 
player freezes for about 4min.

Leo at AGPtek support has been very helpful.  He has referred me to this 
test page.
http://download.wavetlan.com/SVV/Media/HTTP/http-aac.htm
Many of the files there have a .m4a container and the player will play them, 
so the container does not seem to be an issue.  It will even play the 
MediaCoder Test 1 and Test 6 files which are respectively HE-AAC v1 with SBR 
and HE-AAC v2 with SBR and PS.

I have also tried using flashaaclow which gives a bit rate of 48kbit/s and a 
sample rate of 24kHz.  The player will play the resultant .m4a file which is 
HE-AAC v1 with SBR, but it takes about 2min to play a 24min programme.  It 
plays about 6 words, skips and plays another 6 words and carries on like 
that to the end of the programme.

I did have another portable player until it died after two months.  It was a 
GMYLE DAB+ radio and .mp3 player.  It would play .m4a files, but I would get 
a burbling noise every 30s or so.  If I converted the files to .mp3 they 
would play without the noise.  Curiously when I recorded a Polish DAB+ 
channel as .m4a the player played the recording without problem.

Obviously one solution is to convert the .m4a files to .mp3 because they 
then play fine.  On 31 May I asked about the --aactomp3 option.  (Belated 
thanks to everyone who replied.)  I was told I would get better quality if I 
left the files as aac/.m4a than if I converted them to .mp3.  It does not 
seem to be that easy to find a portable player to play the .m4a files.

Any suggestions?