Thanks for the write-up, I have had an interest in the system so am keen to hear more about how it plays out in practice.
Just to contribute, I really love suppressive fire rules. I feel that they really give a pinned-down effect and make machine guns and similar weapons play the way I feel they should. In the instance mentioned of the character wishing to give support to the fleeing civilians, I feel that some good rules for supressive fire could really help there. The best rules I have seen for this are in Shadowrun 5th edition. To bastardize them, I would suggest something like this:
A) You pick an area to lay down suppressive fire in. EG a LMG can do a 5 meter line area of effect, or X squares.
B) Everybody in that area is given the choice to fall prone or dive behind cover. If they don't, you attack them as normal, with a bonus to hit. If they do take cover, you automatically miss them.
C) From here on, until you stop doing it, your gun runs out of juice or overheats, everybody in the suppressed area gets -X to all attacks and cannot move out into the open.
D) At any time, the enemy can choose to not take the - to attack, or to move out into the open. If they do, you get a free shot on them.
The particulars need adjusting for the game of course, but I find that the rules worked really well in my Shadowrun games. It gives people the feeling of being pinned down and having to just take cheaky potshots. It plays out very tactically and makes people fear machine guns as much as they should. I like having a weapon can really change the battle without actually doing any damage at all.
The interactions between this style of suppressive fire and your pinned-down and crossfire rules could be very interesting, but very deadly. The HMG lays down the suppresseive fire, trapping people, while the standard infantry move to outflank. There is a reason that people use grenades, smoke and airstrikes to get rid of machine-gunners.
On a side note, excuse my ignorance, but does the Pinned-down rule make sniper-nests and entrenched positions a little impractical? You would have to give them such a huge bonus to defence to counteract the advantages the attackers get. Would it be an idea to say that an entreched position has X dice resistance to being pinned down? So in a properly made sandbagged machinegun nest or a WWII normandy bunker, you ignore the first 3 bonus dice that the enemy are getting to pin you. I think that this could help distinguish between an encounter where you are storming a defensible position and an encounter where the battlefield just happens to have various peices of debris to take cover behind.
A properly entrenched position would simply ignore the pinned down rule. Some careers are also able to do so - a sniper ignores the rule, for example, as one if his special abilities.