Yes, solenoids could cause this. "Sticky" solenoids will delay sending fluid and delay pressure buildup of the appropriate brakes / clutches to engage specific gears. They are external in the sense that you don't need to dismantle the entire transmission to reach them, but it's a major operation. Most likely you will need to replace the complete valve body. You may try to replace a specific solenoid assembly, but if one is failing, odds are another one will follow soon and you will have to do another intervention.
If you do, make sure to use either new OEM or factory-rebuilt one (don't buy cheap-er knock-off from Amazon or eBay - you will spend more money on labor redoing the job again and again than what you will save on parts).
The Transmission Valve Body Assembly is part #35410-33122, MSRP $1,634.
Individual valve assemblies vary from couple hundred to four hundred (
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Labor will be a few hundred.