The short answer is: I don't.

I have creeps that target moving creeps re-calculate every time they move.
The only real caching options here are: check if the target has moved enough to merit an update, if so recalculate.

Following is my high efficiency caching code.
It uses the builtin path finding and caches very aggressively.

I've run 50+ creeps on 20cpu with this code.

It handles blocked paths by taking a random step+hoping it finds a better cached path. This actually works rather well.
When multiple routes involving the given tile have been cached, the script chooses from them in a weighted random fashion, this keeps all your creeps from clogging up on the same route when they travel at differing speeds.

function routeCreep(creep,dest) {


    if(creep.fatigue>0){
        return -1;
    }
    if(typeof dest == "undefined"){
        return -1;
    }

    var locStr = creep.room.name+"."+creep.pos.x+"."+creep.pos.y

    var path = false;

    if(typeof Memory.routeCache !== "object"){
         Memory.routeCache = {};
    }

    if(typeof Memory.routeCache[locStr] === "undefined"){

        Memory.routeCache[locStr] = {'dests':{},'established':Game.time}


    }
    if(typeof Memory.routeCache[locStr]['dests'][''+dest.id] === "undefined"){    
        Memory.routeCache[locStr]['dests'][dest.id] = {1:0,2:0,3:0,4:0,5:0,6:0,7:0,8:0};
        path = creep.room.findPath(creep.pos,dest.pos,{maxOps:500,heuristicWeight:2})
        if(typeof path[0] !== "undefined"){


        Memory.routeCache[locStr]['dests'][''+dest.id][path[0].direction]+=1;

        for(var i =0;i<path.length-1;i++){
            var step = path[i];
            var stepStr = creep.room.name+"."+step.x+"."+step.y//creep.room.name+"."+step.x+"."+step.y
            if(typeof Memory.routeCache[stepStr] === "undefined"){
                Memory.routeCache[stepStr] = {'dests':{},'established':Game.time,'usefreq':0.0};
            }
            if(typeof Memory.routeCache[stepStr]['dests'][''+dest.id] === "undefined"){
               Memory.routeCache[stepStr]['dests'][''+dest.id] = {1:0,2:0,3:0,4:0,5:0,6:0,7:0,8:0};
            }
            //console.log(path[i+1].direction);
            Memory.routeCache[stepStr]['dests'][''+dest.id][path[i+1].direction]+=1;

        }
        }
        else{

            dir = Math.floor(Math.random()*8);


            var error = creep.move(dir);
            return error;

        }
    }

    for(var k in Memory.routeCache[locStr]['dests']){
        if(Game.getObjectById(k)==null){//clean out invalid routes
            delete  Memory.routeCache[locStr]['dests'][k];
            //console.log("Pruned",k)
        }
    }


    var total = 0.0//pick from the weighted list of steps
    for(var d in Memory.routeCache[locStr]['dests'][''+dest.id]){
        total+=Memory.routeCache[locStr]['dests'][''+dest.id][d];
        }
    }
    var total=total*Math.random();

    var dir = 0;
    for(var d in Memory.routeCache[locStr]['dests'][''+dest.id]){
        total-=Memory.routeCache[locStr]['dests'][''+dest.id][d];
        if(total<0){
            dir = d;
            break;
        }

    }

    if(creep.pos.getRangeTo(dest)>1 && pathisBlocked(creep.pos,dir)){ //you will need your own "pathisBlocked" function!
        dir = Math.floor(Math.random()*8);
    }


    var error = creep.move(dir);
     return error;

}

Essentially, what you are describing is a problem with javascript (and the javascript engine). I agree it is an issue (for errors in game as well) but somebody thought javascript was a good idea and here we are.