While some have pointed out creative ways to carry gear which may indeed allow the removal of the rack, the real key is to carry less. Each of us must decide what is appropriate based on where, when and how long we ride and our personalities / comfort level.
Some cyclists like to prepare for the "worst case" scenario. They enjoy their rides with the knowlede that no matter what problem comes up, they are likley to have the solution. Hence the racks, large bags, extensive tool kits, multiple tubes, maybe a spare foldable tire, extra clothes, extra food etc. Many have chosen to buy their bikes with couplers because they may wish to travel with their bike some day.
My stoker and I try to be prepared for 98% of the problems that we are likley to encounter and then live with the consequences. We have two seat bags on our tandem, no rack or other bags. Mine is very small and carries a spare tube, a tube patch, a 1-1/2"x5" piece of tyvek envelope for a boot, two tire levers and a small multitool that is about 1/2" diameter and 3" long. The multitool has interchangable heads in an inner chamber and I removed the ones that do not work with fittings on our bike. The pack also carries a micro inflator and one co2 cartirdge. We carry a micro pump that attaches to water bottle braze ons without preventing a water bottle cage to be attached. In my entire life of riding I have had two flats on one ride twice. Perhaps some day I will have a third, but so far, my approach with a tube, a patch, one co2 and the micro pump has never been inadequate.
My stoker's set bag is also small but we are considering getting one a little bit larger to carry more food on unsupported rides when we cannot or do not want to stop to buy food - 150 miles or so. She carries one clif bar for each of us, plus one sleeve of shot blocks for each hour that we will be riding. It also carries, her cell phone, a bit of cash, a credit card, and a very small combo luggage lock and very short cable intended to allow one to lock a saddle with QR seat tube or a helmet to a bike that might have another lock. With this short cable and luggage lock I am able to lock our bike and helmets if we stop somewhere for a beer or a lunch. Definitely not theft proof, but it does deter the opportunist. So far we have never had to use the cell phone and credit card to get back home, but it may happen some day and will probably be a bit of a hassle but I am ok with that. I'll either wait with the bike or join her in the cab and take my chances with my little lock and cable depending on where we are located and the problem with the bike.
Like others we have used our 4th water bottle (I bought the largest I could find), to carry / store wind breakers on occassion or perhaps to carry food for a picnic. Can't carry a box of fried chicken but wraps or thai sandwiches fit beautifully. Like I said, we live with consequences, but we can make adjustments.
Getting back to the original question, and thinking about the OP approaching the final climb at Solvang and looking for a little psycological boost - how many times have you finished a ride with a couple of mostly full water bottles? My wife and I cary four bottles on long rides and always seem to have plenty left over as we fill when we stop - "just in case". Although I have never done this and probably never will, because I am not as concerned about a few lbs as some riders (and I certainly do not pass judgement on them - I have a whole different set of quirks) you could have your stoker dump all remaining water as you approach the bottom of the hill. A 24 oz bottle is pretty common, some are larger so if you dump two full bottles = 48 oz that's three pounds right there. When you get ot the top if there is a stop or at the finsih line drink all you want.
Yes I know it is off the table, but for others who may be thinking about this problem, I'll share one last bit of info. Thinking about those climbs at the end of a long ride can be a great motivator. We are not super high milers like many here but ride a half dozen or so centuries each year. My wife wants to ride STP in one day. Overall it is pretty flat but there are some hills toward the end of the 204 mile ride. Thinking about those last climbs has given us motivation to try to lose some significant lbs from our load. So far I am down 15 lbs and she is down about 7 lbs for a total of 22 and we hope to double that by the time of the event. We have dabbled with losing lbs for years but lowering our climibng weight has become a big motivator and finally we are having success.