You're used to the island materials coming and providing a significant source of materials. This is not an accurate representation of how Lost Ark is once you reach the current tier of content available. The added material from islands is a catch up mechanic that was put in place after the content had been released for some time; you are effectively 'caught up' to the end game at 1345, which is to say that progression is now going to be significantly slower. For the sake of your sanity, you should immediately cease thinking that you're going to be seeing power increases at anywhere near the rate that you were previously. You may have thought the last few upgrades before hitting T3 was slow. That was nothing compared to what's coming. In EQ terms, you're now max level for the expansion with decent dungeon gear; your character is still going to progress via a raid drop from time to time but this is a process of upgrades that is going to take weeks/months per upgrade rather than hours/days.
In addition to the sources you listed, there is;
1- Guild merchant
2- Pirate ship
3- Abyss Dungeons
4- Infinite Chaos
5- Alts (more on this below)
Sooner rather than later, they'll also add the PVP vendor for rewards, which is an additional weekly source of materials.
April will also release South Vern, which is a continent that will bring several significant source of materials in short order, specifically;
1- Heoic Guardian Raids
2- Abyss Trials
3- The bridge
4- Legion raids & Rehearsal raids
Lastly, there was a lot of discussion on the chat throughout the weeks as it relates to alts. Several people noted that they didn't feel that alts provided a significant acceleration (via trading materials). This was true in T1/T2 however, now that you're in T3, this sort of changes. Alts become a very large source of added materials for the purposes of pushing your main up. Some people thought I was exaggerating when I said that it would have been quicker for me to re-do 0-1345 than 1345-1370. It wasn't. You are going to hit a point where the upgrade chance is 10% per attempt, with an increase of 1% per failure until you hit the pity, which takes a lot longer. The cost of gold/silver per attempt is also higher, so you'll be capped on attempts from other sources. I mention this just to make it clear since a lot of the guild is hitting the 1340 point now: shift your expectations for how quickly your character is going to progress. It's going to be a much longer journey. Thankfully, there are a myriad of other ways to also increase your character's power (skill points, engravings, accessory optimization, etc).