You did two good things here. You recognized there was an issue to figure out. And you came up with a tree which is reasonable. You could use that tree in a discussion and it wouldn’t screw up the discussion. It corresponds fine to what the writer meant.
Here’s the process I used for analyzing the tricky part of this sentence:
- Notice there’s an issue (there appear to be two nouns after the verb)
- Consider if one of the nouns could be an indirect object.
- Come up with a couple reasons it’s not an indirect object.
- Look up “last” and “spring” in a dictionary.
- Web search something like “last spring grammar”.
- Skim a relevant forum topic this which linked to a different dictionary entry.
- Conclude it’s a special case. The dictionary gave some rules for when to omit a preposition but gave no conceptual explanation. So I don’t know why exactly but I concluded that this sentence simply doesn’t follow standard grammar rules. Adding an implied preposition in the tree to fix it is fine.
I suggest trying to go through this process yourself.