You really can't beat the FBS/BBS technology of the Minelabs, especially on the beach, so to makes things easier, I'd stay with Minelab for now. Garrett don't do multi frequency detector, and Whites only current version that has anything similar to the Minelabs is the V3i, which is quite a complex machine, with a plethora of user settings to get your head around.
The Excalibur is definitely the weapon of choice for most pro beach & surf hunters, the Safari lacks the ferrous/conductivity and smartfind readout that the Explorer, Etrac and ctx have (ctx is a bit more involved), they are very useful features for identifying in-ground targets.
Bigger coils don't necessarily equate to more finds, in fact trashy areas beg for much smaller coils to get decent target separation. If you can't distinguish seperate targets with the eliptical DD coil on the 705, then you certainly aren't going to find it easier with an even larger coil again. In fact the smallest coil I have for the Explorer is exactly the same size as the 705 gold coil, that is my go to coil for really junky areas. I wouldn't want to use anything larger than the 11" coil for general park hunting, but a larger coil may be beneficial on the beach.
Patience is a necessity for detecting, it is just a fact of life. There are a lot of people with the most expensive detectors on the market, and have very little in the way of finds to show for such a huge outlay, mainly due to them either not spending enough time on the ground to intinitely know their detector and what it is telling them, plus not knowing the best areas to detect at. Despite the Bogan crew having a very capable detector in the CTX, I can assure you that much research has gone into the areas they detect, along with a decent amount of time in the field to get the best out of their detectors.
Whilst any of the above mentioned multi-frequency detectors will give you an advantage over the 705, especially regarding depth and capability on wet wet sand or in the surf, you will still find that you will have research the tones and vdi no.s, just as you would have on the 705.
If I was to do parks, dry sand/wet sand, the Etrac would be fine, if going anywhere near the water, then Excalibur or CTX - or of course, the CTX for everything. If looking at gold prospecting as well, I would look at a completely different detector again.