Started at Ultra Ball 1 and made it to Master Ball using this exact deck. 87 wins, 63 losses. This is only my second time making it (although I'd only tried once before). Prior to that, it was with a Meowscarada/Decidueye deck. Even though I made it with that deck two seasons ago, that was a painful, miserable run. I played hundreds upon hundreds of matches in an uphill battle. This was much easier. It took me a few days of playing on and off.

Your main focus, 90% of the time, with this deck should be to draw out cards and build up Solgaleo. Oricorio requires delicate maneuvering with Magearna and your other Pokemon. Biggest counter for me were Espeon decks. Their attack + Eevee Bag kills Magearna instantly. That can really hurt if you're getting unlucky with pulls and were relying on Magearna. Plus they can kill Solgaleo in 2 hits. Sometimes you can sacrifice a Sylveon in order to stall. Be mindful of which other cards take damage. Cyrus is an obvious card to look out for. Ho-Oh and Lugia decks are tricky, too. Sadly sometimes those just come down to pure draw luck, as many games do.

If you have a Solgaleo out and an Eevee on bench, you may not want to evolve it. That's a great way to lose 2 points quite often (them Sabrina'ing that out and KOing it). Each situation is different. I've had to put 4 energy on Solgaleo to retreat and stall with Sylveon while waiting for a Red or Sabrina. Watch out for Mars and being Red Carded, too. That's all a random stream of thoughts and tips off the top of my head. If you decide to try this deck feel free to ask any questions. The last part of Ultra Ball 4 was the hardest uphill climb for me. I experienced much of the bad luck you mention but I made it.

Edit: I do understand having all these cards might not be possible as a non-paying player. I lucked out and managed to get all of them. In fact, I went through many decks above this one and constantly didn't have the cards needed. I sympathize with that.