Understand - dozens of TWS pings is not "just looking around". It's "we're gonna get you, better do something about it". What that something is depends on tactical situation.
And is not pointed towards the target, since the missile is not flying a direct path. The datalink signal doesn't have to bounce all the way back, so the power is much lower than the main signal. Thus, you can forget about detecting sidelobes.
Further more, what makes you so sure that the new Flankers need to STT all the way for SARH? The much older Zaslon will happily guide 4 SARH at once, to sepparate targets. Now, that may be partially due to missile design, but doesn't mean that something can't be done to optimize other missiles without this built in. All the missile needs is datalink in first stage, and STT when it goes auto.
Even Su-27's Zhuk had a 'secret lock' mode (Russian versions only), to make the other guy think it is still in search mode, while it's actually STT.