Can you have both Attribute modifiers and displays on an item? [duplicate]

I'm making an adventure map where I have a Villager "merchant" that sells custom armour for the price of a custom currency (All of this works fine. In a previous arqade question (You can see it here) I had a problem with this but it works like a charm) I wanted to add another feature to this armour now that i have the villager working. Lone behold, I have yet another issue. I have tried fiddling around with tags and formatting. Nothing seems to be able to allow me to have a villager that sells a custom named item that also has it's own modified attributes. It seems I can only have the item to have a custom attribute (but no custom display) or a custom display (but no custom attributes) My current command displays a custom name and lore but has no attributes:

/summon villager ~ ~1 ~ 
{
CustomName:"Lv.1 Gear Merchant"
,CustomNameVisible:1b
,NoAI:1b
,Invulnerable:1b
,Offers:
{
Recipes:
[
{
buy:
{
id:"minecraft:gold_nugget"
,tag:
{
display:
{
Name:"Gold Coin"
,Lore:
[
"$1"
]
}
}
,Count:32
}
,sell:
{
id:"minecraft:leather_chestplate"
,tag:
{
display:
{
Name:"Shoddy Leather Jacket"
,Lore:
[
"Lv.1"
]
}
}
,Count:1
}
,tag:
{
AttributeModifiers:
[
{
AttributeName:generic.maxHealth
,Amount:1
,Operation:0
,Name:Health+
,UUIDLeast:999
,UUIDMost:999
,Slot:"chest"
}
]
}
,maxUses:9999999
}
]
}
}

Again in this draft I have no errors, it just doesn't seem to want to apply my attribute changes. I created another draft that seemed to result in the exact opposite. The command:

/summon villager ~ ~1 ~ 
{
CustomName:"Lv.1 Gear Merchant"
,CustomNameVisible:1b
,NoAI:1b
,Invulnerable:1b
,Offers:
{
Recipes:
[
{
buy:
{
id:"minecraft:gold_nugget"
,tag:
{
display:
{
Name:"Gold Coin"
,Lore:
[
"$1"
]
}
}
,Count:32
}
,sell:
{id:"minecraft:leather_chestplate"
,tag:
{
AttributeModifiers:
[
{
AttributeName:generic.maxHealth
,Amount:1
,Operation:0
,Name:Health+
,UUIDLeast:999
,UUIDMost:999
,Slot:"chest"
}
]
}
,display:
{
Name:"Shoddy Leather Jacket"
,Lore:
[
"Lv.1"
]
}
,Count:1
}
,maxUses:9999999
}
]
}
}

Now the health is working but the display is kaputz. This feels like a game of whack-a-mole that's making me pretty TRIGGERED. Anyways, I suck at commands and hopefully with the help of anyone who sees this, I can learn. Thanks.

In both of the commands you posted, you made a mistake. In the first one you had this:

sell: {
    id: "minecraft:leather_chestplate",
    tag: {
        display: {
            Name: "Shoddy Leather Jacket",
            Lore: ["Lv.1"]
        }
    },
    Count: 1
},
tag: {
    AttributeModifiers: [
        {
            AttributeName: "generic.maxHealth",
            Amount: 1,
            Operation: 0,
            Name: "Health+",
            UUIDLeast: 999,
            UUIDMost: 999,
            Slot: "chest"
        }
    ]
},

In the second one you had this:

sell: {
    id: "minecraft:leather_chestplate",
    tag: {
        AttributeModifiers: [
            {
                AttributeName: "generic.maxHealth",
                Amount: 1,
                Operation: 0,
                Name: "Health+",
                UUIDLeast: 999,
                UUIDMost: 999,
                Slot: "chest"
            }
        ]
    },
    display: {
        Name: "Shoddy Leather Jacket",
        Lore: ["Lv.1"]
    },
    Count: 1
},

The AttributeModifiers and the display need to go inside the same tag, and it has to be inside the sell item. This is your corrected command:

/summon villager ~ ~1 ~ {CustomName:"Lv.1 Gear Merchant",CustomNameVisible:1b,NoAI:1b,Invulnerable:1b,Offers:{Recipes:[{buy:{id:"minecraft:gold_nugget",tag:{display:{Name:"Gold Coin",Lore:["$1"]}},Count:32},sell:{id:"minecraft:leather_chestplate",tag:{display:{Name:"Shoddy Leather Jacket",Lore:["Lv.1"]},AttributeModifiers:[{AttributeName:"generic.maxHealth",Amount:1,Operation:0,Name:"Health+",UUIDLeast:999,UUIDMost:999,Slot:"chest"}]},Count:1},maxUses:9999999}]}}