I think embroidered or Bevo insignia is ok for just about the whole war, just as long as its not the subdued varients. Although the embroidered would be previlant early on, Bevo would perhaps be more common overall. However the M40 sidecap I don't think was used by the Heer- they continued to use the M34 while the SS and LW switched to the M40. 
I would go for BeVo every time - even though you can get wool cap insignia, I'm not sure it was actually ever made.
Sorry to contradict you Lardy, but looking at Brian Davis' book, it seems that the M40 (sometimes also referred to as M42!) was also commonly used by Heer.
You've got nothing to ein, zwei, drei, vier
Sorry to counter- contradict you Steiner but the M40 & M42 were 2 different caps. 
The M40 was like the M34 but without the scooped turn up at the front. The M42 was essentially the M43 cap without the peak. I'd like to see those pics you have if possible as I didn't think the Heer used the M40 style at all, except for possibly some panzer versions.
You're probably right on the insignia though, BeVo is the safest bet.
[*begins search... no matter how long it takes...!*] 
You've got nothing to ein, zwei, drei, vier
Bucket 'o' caps...
[link]http://web2.airmail.net/recon36/german/heer/heercaps.html[/link]
Lardy could be right..... 
You've got nothing to ein, zwei, drei, vier
I think he is.
Wool insignia on caps is one thing I have spent a long time looking into. Almost without fail the Heer infantry M43 had bevo, the SS and Lufty used bevo and wool. There are some images of the heer panzer M43 with wool but they are rare.
As a rule of thumb I'd say go with bevo as you cant be wrong.
aka Stigroadie
AFRA
better by design
"Truth is a shining goddess, always veiled, always distant, never wholly approachable, but worthy of all the devotion of which the human spirit is capable. "