If you want to stop funding wars, or even just the escalation of wars, the easiest way is to just not fund them. This can be done in the House alone. The Senate is not needed. The president is not needed. Rather than passing a bill stating that you won't fund wars, and then dreaming about getting the Senate to pass it too, you can choose to not pass bills that fund the wars. If the House makes clear that it will not fund an escalated war, then the war cannot be escalated. If the House makes clear that it will not fund a continued war, then the war cannot be continued.