It is impossible to second guess the metrics that Airlines use for employing pilots. The favoured background tends to be whatever route the person doing the employment took and that varies enormously from company to company. One way to move forward with an airline is to work for them in another capacity - anything will do - and that way they will know you are not an employment risk. I know a number of pilots that fly big shiny jets that used to be dispatchers, flight attendents, ops staff etc and made the transfer when the company needed pilots.
The biggest influencing factor in a company hiring pilots is "dammit, we don't have enough pilots and we just lost a revenue sector because we were short of a driver. Get some more jeeves" and right now thats not happening. Most companies are clinging on for grim death and just trying to bleed cash at a sustainable rate.
Times aint good - fly anything you can and stay busy. I don't agree that you can have too much time on a twin or instructing. If the economic environment is poor an employer will be interested in the fact that you stayed in the air. If you can't do that, they will be interested if you did something else that was interesting (don't sit and watch tricia). It took me years to get my first proper job so keep the faith.