A big syringe I would think could push it. Not sure how I would get the crap out of the reservoir with fluid still covering the hole and keep air from coming back in. Curious to see how that works.
I just do brake bleeding and clutches the same, vacuum (hand pump) from caliper or slave cylinder while ensuring there's enough fluid in the reservoir. If my lever still comes back softer than it should (subjective assessment for sure), I ty-wrap the lever as close to the bar as wants to go and leave it over night. It's usually solid after that. If it comes back to the bar before you want to use the ty-wrap, you need to re-bleed them until it doesn't. Has worked repeated with bleeding systems with ABS as well.
There's probably better ways but this has proven fast and reliable for me. Good luck.
2004 BMW R1150SR Project Touring Bike (in-work)
2005 Honda RC-51 SP-2 - future track tool
2014 Ducati HyperProject (Hyperstrada)