done it post Brighton Fridays several times as far north as the 'sham on 28's with, so far, one pinch flat. Nice pub at The Partridge. Partridge Green for refreshment. They sell Dark Star Brewery jerseys behind the bar. My touring bike has done the whole length several times without issue apart from rattling the mudguards. A lot.
But it you pootle over to Shoreham and take the road up to Steyning and then go up to Horsham via Ashurst it's a lovely ride. Then go to Guildford via Cranleigh and you miss the horror that is the A281. Much faster than the downs link.
Were it me I'd go probably go Brighton, Waterhall, A23 cycle path jobbie, Aldbourne, B2116, Partridge Green, Littleworth, Nuthurst, the 'sham, Rowhook, Ellen's Green, Cranleigh, Rowly, Shamley Green, Wonersh, Glidfud. and keep my fillings intact. Post lonjog there isn't a climb on that route will faze you.