Use beads to which the antibody is covalently attached. That way, when you elute the beads with SDS-PAGE sample buffer, the heavy chain will stay with the beads.
You can use light-chain specific secondary antibody or proteinG-HRP as secondary antibody which should only recognize primary antibody in native form (antibody used for IP is denatured while that used in WB is native).
I've done a substantial amount of work optimizing IPs.
Covalently binding antibody to beads can be useful, but there are a few caveats.
First, chemical crosslinking of antibody to beads (DSS or BS3) can reduce the activity of the antibody and decrease pulldown efficiency.
Second, non-chemical-crosslinking of antibody to beads (like the Dynabead surface activated epoxy beads) can avoid the reduced activity that chemical crosslinking causes. If your antibody contains contaminants (azide, glycerol, BSA, serum factors, etc) it will reduce crosslinking efficiency. An antibody cleanup step might be necessary.
You could alter IP and elution buffer conditions. Excluding DTT and heat can reduce the possibility of the IgG detaching from beads during elution.
The easiest way to reduce the IgG heavy chain band is to use a secondary antibody that detects only native IgG. We use CleanBlot by Pierce and have had great success. We've actually switched from crosslinking antibody to beads to just using the CleanBlot secondary. It is not only a cheaper but also a more convenient option.