I can tell you from personal experience that traffic in LA is pretty bad on a regular basis. The times that are off-peak for traffic on the East Coast are often clogged with traffic in LA. Saturday morning at 7 am often has more cars on the road than you could imagine so I would not expect a holiday to necessarily mean a lot less road traffic. 5:30-6 pm on a regular weekday is rush hour time so you won't be making any quick progress.

Hyatt Long Beach is about 22 miles from LAX. The Super Shuttle runs about every 10 minutes from LAX (and you don't need an advance reservation). I went to their website to price the fare and it came out to $17/person each way. A cab will cost at least 5 times that amount based on this website. You are looking at a fare of roughly $65 for the distance alone plus whatever time you sit in traffic, and you are expected to tip on top of that (10-15 %). 22 miles at $2.70/mile + $2.85 flag for the first 1/9 of a mile + $2.50 surcharge from the airport = $64.75. Every hour you wait in traffic is another $29.19 ($0.30 for every 37 seconds). A quick trip with little traffic will probably have at least 10 minutes wait time, so you are looking at a fare of about $70 in the best case. In the worst case you could be stuck with a one hour+ delay, and that would push the fare to $95 or more depending on the delay length.

The quote for the shuttle also showed the cost for a private car, a private van, and a smaller, private van of $100 (4 passengers), $85 (9 passengers), and $58 (5 passengers), respectively.

The shuttle is the cheapest option, but the exclusive minivan is the best if you want to get to the hotel as fast as possible and save some money. A private car is preferable to a cab since the fare is fixed.