What is the best way of conveying respect to elders in English?

I think you is the polite form (u). The less polite form is thou (jy), but us Brits, polite as ever, now call everyone by the the polite form and thou fell by the wayside a long time ago.

Thou barely ever surfaces in normal English unless you want something to sound historical, but it is still in Holier than thou and used to be (20th century) common in regional dialects from Yorkshire and parts of the Midlands (anyone can feel free to correct my geography).

So you shouldn't feel so bad using you it's not the same you (jy) that you think it is.

You haven't stated where you are currently located (if not in South Africa); how your question should be answered will depend both on your location and your social setting. So I will respond in general terms.

You should be aware that in the USA, the UK, Canada, Australia and New Zealand at least, expectations of social deference and the conventions of traditional hierarchy are generally much less pronounced today than they were before the social upheavals of the mid-20th century -- especially, perhaps, within the bounds of individual social milieus.

You could nevertheless sprinkle your exchanges with those to whom you wish to demonstrate respect with the occasional sir and ma'am (especially in the southern states of the USA, where some of the older formulations of gentility still cling on to some degree); this in addition to the instances of "excuse me", "please" and "thank you" which I'm guessing already come naturally to you.

Just be aware that where such obvious signals of deference are not usually expected (as in the UK, for instance), it can be almost as easy to alienate one's audience through over-politeness as through over-familiarity. If I addressed one of my parents the way you apparently address yours, they would wonder (probably rightly) what was wrong with me. Generally speaking, if you just exhibit general considerateness towards the person you are talking to you won't go far amiss.

Your statement, "The lack of English equivalent [to third-person modes of address] feels very wrong and disrespectful" seems to me to be overlooking one of the most important factors connected with a successful interaction -- namely, the necessity to help your interlocutor to feel at ease rather than to focus on your own conceptions of what you think polite behaviour ought to consist of.

Such a result is achieved differently in different social and geographical settings; bear in mind that the conventions and social institutions that exist in American and British society (etc.) are considerably different to those of South Africa.

Same in Dutch when I was growing up. That's been disappearing rapidly in the past two decades. I started noticing when my mom insisted that she wanted to be addressed as jij instead of U. Took me a while to get used to :)

"You" in English used to be the equivalent of U, 2nd person plural pronoun (jullie in Dutch). Same idea as the French "Vouz". "Thou" used to be 2nd person singular, equivalent of jij. The distinction has disappeared completely and thou became archaic and often misinterpreted as the formal form. You can't say "How art thou?", it sounds respectful but will draw some funny looks :) You can say "How are you today, Sir" if you want to but it is hardly necessary. You'd use it in a chat with the President.

The loss of a distinctive 2nd person plural pronoun in English is pretty painful to a Duch guy like me that's got it ingrained in the brain. I'm not alone, it is a problem that's solved with regional variations. Y'all is popular in the Southern USA, "You guys" is pretty well spread, "Youse" has pockets of usage. I personally liked "Yunz" near Pittsburgh, not infrequently mangled into "Yunzes" :) Much to the chagrin of my wife that grew up near there and still considers it an abomination, so I have to use y'all.

I think the US, respect tends to be expressed with posture, attitude, and content of what you say rather than with the use of specific words. Formalisms such as specific honorifics tend to feel stilted (although as others have noted, there are regional variations), but wouldn't be offensive.