Jomsviking, I am glad that this problem is being discussed and moreover, you inspired me to speculate around solving it too! :)

I would suggest:

1) Your empire has "war tiredness" (any synonym) stat which depends on militarist-pacifist balance and your casualties over X turns. When war tiredness exceeds its limit, you begin increasingly loosing influence each turn AND empire approval slightly decreases. If you are out of influence, you (your senate) automatically sends "fair" truce proposal to ALL your foes (starting with those who have best win score) at the end of the turn if you did not negotiated it yourself. If you have nothing to propose for a fair truce, your empire approval decreases significantly. Casualties from an adversary who declared war on you (or is an ally of an aggressor) have less impact upon war tiredness progress (defensive war effect). The same is actual for casualties from a foe who occupies systems which were first colonized by your empire (irredentism effect). Pacifist-ruled senates also give aggressive war turn counter which is to be added to casualties effect - in case the war was declated by that pacifist empire. Once a truce is declared, you recover from casualties caused by THIS faction over 10 turns. 

Consequently:

1) If war goes extremely well (no casualties on your side), your people don't oppose such a war.

2) Significance of influence rises. At the moment, it is a very underpowered resource since mid-game.

3) Militarist-pacifist distinction is better represented. Surely, rebalance will be required in favour of pacifists and against militarists.

4) Problem of unpredictability of forced truce is solved.

5) Bilateral peace treaties did not make sense: if your senate is tired of war, why to make peace with only one enemy? As Vodyani, I had to delay a war against my second neighbour just because I would skip X turns of abduction since truce begins. So weird.

6) More interesting military policies: provoke an adversary to declare war so that you had a justification for annexation; get pacifists out of the senate so that they could't undermine the people's morale; attack a stronger enemy suffering from war protests and force him to give you an easy tribute.

7) Referring to the initial suggestions: this way does not imply inherent racial features; as for Cravers, they can avoid war tiredness indirectly: through racial inclination to militarism and factual militarist behaviour of a player.

The formula for that mechanic would look like that:

MP=Militarist Population% * 0,7

MS=Militarist Senators % * 0,3

PP=Pacifist Population % * 0,7

PS=Pacifist Senators % * 0,3

OP=Other Population % * 0,7

OS=Other Senators % * 0,3

MC=your Command Points lost over latest 20 turns (military casualties)

CC=your Population killed over latest 20 turns (civil casualties)

OS=Once your population in Systems that are now Occupied by enemy.

D=Defensive war? Yes=0,6; No=1

I=Irredentist war? Yes=0,8; No=1

PS=Pacifist-run senate and you are the one who declared the war? Yes=1;No=0. Multiplied by game speed and FIDS (cannot tell formula now).

N=# of turns the war is conducted.

T=War tiredness which is separately counted for war with each enemy (T1, T2, T3, etc).

TT= Total tiredness, a sum of all T

TL=Tiredness Limit, derivative of FIDS

IL=Influence lost per turn after TL is reached, derivative of FIDSI (cannot tell formula now)

AL=Approval lost per turn after TL is reached = 1

AL2=Approval lost per turn after event of influence deptition = 5

T=(MC+CC*2+OS)*((MP+MS)*0,75+(PP+PS)*1,25+(OP+OS)*1)/200*D*I) + PS*N

The forced truce shouldn't be in the game. Especially not with NPCs.

Not only does it prolong the Game, it also is incredible bad game design since their seems to be no counter play. Combined with the closed Borders, they can lock up whole armies of yours in a system.

Not only has it no counter play but I also don't get how it integrates with the lore. Who forces the truce on you, exactly? And why do I only receive a paultry amount of dust for it and can no make my own demands? I mean, ~80 dust over x turns is nothing, if just repairing ships costs way more.

Forced Truce would be ok as an ability for a pacifist - diplomatic empire, but giving it to nearly everyone (even Cravers use forced truce on you ...) is just bad form. Made my Craver playtrough incredibly unsatisfying.

If you must integrate it, at least consider that you could easily break the truce with the penalty that all other factions have worse relations with you.