Of course, west.
As to extending the war. Hungarians committed something between half and 3/4 of their army in Ruthenia and Eastern Slovakia. They still had to watch Romania and Yugoslavia, even if they are not obliged to move as Czechoslovakia ceased to exist.
As to Slovak army. It was small and not organized. Unsupplied? Hardly. They got more equipment at the time then they needed.
So I am not so sure of Hungarians attacks on wider front. Of course, if it went to extended war not just at east but also all along the border, they would eventually win. It would take time, it would cost equipment, which Hungarian army was lacking (not enough to supply new units), lack of ammunition. But eventually, they would win. But the cost?
Well let say after eastern part, which are pretty much lowland fell, let say Bratislava goes, let say Trnava goes. That's all lowland. And that's all was lost actually in August 1944, afterwards 2 months of warfare against experienced German troops went on. Would be unexperienced Hungarian army able to push there? Maybe, but it would take not 2 but 3 or 4 months and with nubers at the end they would win.
Afterwards? Maybe no 2nd Wiena agreement, as Romanians would be laughing at their face, their participation on war against Yugoslavia could be even more symbolic or non (which at the end wouldn't be so bed for Hungary

)
The think is, after Hungarian attack Slovak population actually lined up behind the government, which was not really popular even with declaration of independence. Mobilisation was going on, volunteers were coming. It didn't went that way just 6 month later against Poland. There they fielded around 200 000 men all together, but war was not popular. War against Hungary, or actually, defensive war against Hungary was seen in different way.
But yes, it was not in German interest let Hungarian go all wild against Slovakia. Existence of Slovakia made actually German occupation of Czech lands basically legal.